%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO597+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:18:15 PM UTC 2026
% Result : Theorem 182.71s 23.88s
% Output : Proof 182.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 102
% Number of leaves : 38
% Syntax : Number of formulae : 373 ( 225 unt; 0 def)
% Number of atoms : 625 ( 222 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 435 ( 183 ~; 177 |; 37 &)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 1266 ( 124 sgn 560 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t242,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t304,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(orient,[status(thm)],[t242]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t186,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t306,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t186]) ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD21) ).
fof(f20_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t183,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t312,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t183]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(t153,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t346,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t153]) ).
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t193,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t285,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t193]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t125,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t292,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t125]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t180,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t271,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t180]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t117,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t268,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t117]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t118,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t266,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t118]) ).
fof(f55,axiom,
! [A,B,M,O] :
( ( perp(O,M,A,B)
& midp(M,A,B) )
=> cong(O,A,O,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD55) ).
fof(f55_nnf,plain,
! [A,B,M,O] :
( cong(O,A,O,B)
| ~ perp(O,M,A,B)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [M,A,B,O] :
( cong(O,A,O,B)
| ~ perp(O,M,A,B)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c55,plain,
( cong(X3,X0,X3,X1)
| ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(t177,plain,
ifeq(midp(X1,X2,X3),true,ifeq(perp(X4,X1,X2,X3),true,cong(X4,X2,X4,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(t323,plain,
ifeq(midp(X1,X2,X3),true,ifeq(perp(X4,X1,X2,X3),true,cong(X4,X2,X4,X3),true),true) = true,
inference(orient,[status(thm)],[t177]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD7) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t124,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t293,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t124]) ).
fof(f74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD74) ).
fof(f74_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c74,plain,
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(t213,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(perp(X5,X6,X7,X8),true,perp(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t301,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(perp(X5,X6,X7,X8),true,perp(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t213]) ).
fof(f46,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD46) ).
fof(f46_nnf,plain,
! [A,B,O] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [O,A,B] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
( eqangle(X2,X0,X0,X1,X0,X1,X2,X1)
| ~ cong(X2,X0,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(t147,plain,
ifeq(cong(X1,X2,X1,X3),true,eqangle(X1,X2,X2,X3,X2,X3,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t282,plain,
ifeq(cong(X1,X2,X1,X3),true,eqangle(X1,X2,X2,X3,X2,X3,X1,X3),true) = true,
inference(orient,[status(thm)],[t147]) ).
fof(f52,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD52) ).
fof(f52_nnf,plain,
! [A,B,C,M] :
( cong(A,M,B,M)
| ~ midp(M,A,C)
| ~ perp(A,B,B,C) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [A,B,C,M] :
( cong(A,M,B,M)
| ~ midp(M,A,C)
| ~ perp(A,B,B,C) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c52,plain,
( cong(X0,X3,X1,X3)
| ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t178,plain,
ifeq(perp(X1,X2,X2,X3),true,ifeq(midp(X4,X1,X3),true,cong(X1,X4,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(t298,plain,
ifeq(perp(X1,X2,X2,X3),true,ifeq(midp(X4,X1,X3),true,cong(X1,X4,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t178]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(t228,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t333,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t228]) ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD69) ).
fof(f69_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f69]) ).
fof(f69_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f69_nnf]) ).
cnf(c69,plain,
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(hi69,axiom,
ifeq(midp(X0,X1,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c69]) ).
fof(f94,conjecture,
! [A,B,C,O,M,N,NWPNT1] :
( ( circle(O,A,N,NWPNT1)
& coll(N,O,M)
& midp(M,B,A)
& circle(O,A,B,C) )
=> eqangle(A,C,C,N,N,C,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416059) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,M,N,NWPNT1] :
( ( circle(O,A,N,NWPNT1)
& coll(N,O,M)
& midp(M,B,A)
& circle(O,A,B,C) )
=> eqangle(A,C,C,N,N,C,C,B) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,M,N,NWPNT1] :
( ~ eqangle(A,C,C,N,N,C,C,B)
& circle(O,A,N,NWPNT1)
& coll(N,O,M)
& midp(M,B,A)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk20,sk22,sk22,sk25,sk25,sk22,sk22,sk21)
& circle(sk23,sk20,sk25,sk26)
& coll(sk25,sk23,sk24)
& midp(sk24,sk21,sk20)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26])],[f94_nnf]) ).
cnf(c114,plain,
midp(sk24,sk21,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
midp(sk24,sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h5,plain,
coll(sk24,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi69,hi114]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h20,plain,
coll(sk24,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h105,plain,
coll(sk21,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h20,h20]) ).
cnf(h398,plain,
coll(sk21,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h105]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h1315,plain,
coll(sk24,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi1,h398]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h9,plain,
midp(sk24,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi114]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h63,plain,
cong(sk24,sk20,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi68,h9]) ).
cnf(h6,plain,
cong(sk24,sk21,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi114]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
ifeq(cong(X0,X1,X2,X3),true,ifeq(cong(X2,X3,X4,X5),true,cong(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h860,plain,
cong(sk24,sk21,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi24,h6,h63]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(hi67,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(coll(X0,X1,X2),true,midp(X0,X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(h19531,plain,
midp(sk24,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi67,h860,h1315]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD63) ).
fof(f63_nnf,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [M,A,B,C,D] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( para(X0,X2,X1,X3)
| ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi63,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X0,X3,X4),true,para(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(t50,plain,
para(sk20,sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi63,h9,h19531]) ).
cnf(t2282,plain,
para(sk20,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t50]) ).
cnf(t2301,plain,
true = ifeq(midp(X1,sk20,sk21),true,ifeq(true,true,ifeq(para(sk20,sk21,sk21,sk21),true,midp(X1,sk21,sk21),true),true),true),
inference(cp,[status(thm)],[t333,t2282]) ).
cnf(t46,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t46]) ).
cnf(t30737,plain,
true = ifeq(midp(X1,sk20,sk21),true,ifeq(para(sk20,sk21,sk21,sk21),true,midp(X1,sk21,sk21),true),true),
inference(step,[status(thm)],[t2301,t256]) ).
cnf(t30738,plain,
true = ifeq(midp(X1,sk20,sk21),true,ifeq(true,true,midp(X1,sk21,sk21),true),true),
inference(step,[status(thm)],[t30737,t2282]) ).
cnf(t30739,plain,
true = ifeq(midp(X1,sk20,sk21),true,midp(X1,sk21,sk21),true),
inference(step,[status(thm)],[t30738,t256]) ).
cnf(t26324,plain,
ifeq(midp(X1,sk20,sk21),true,midp(X1,sk21,sk21),true) = true,
inference(orient,[status(thm)],[t30739]) ).
cnf(t171,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t272,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t171]) ).
fof(f57,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD57) ).
fof(f57_nnf,plain,
! [A,B,P,Q] :
( perp(P,A,A,Q)
| ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f57]) ).
fof(f57_sk,plain,
! [A,P,B,Q] :
( perp(P,A,A,Q)
| ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f57_nnf]) ).
cnf(c57,plain,
( perp(X2,X0,X0,X3)
| ~ cyclic(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(t237,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,ifeq(cyclic(X1,X3,X2,X4),true,perp(X2,X1,X1,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(t270,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,ifeq(cyclic(X1,X3,X2,X4),true,perp(X2,X1,X1,X4),true),true),true) = true,
inference(orient,[status(thm)],[t237]) ).
fof(f12,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD13) ).
fof(f12_nnf,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [O,A,B,C,D] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( cyclic(X0,X1,X2,X3)
| ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(cong(X0,X1,X0,X3),true,ifeq(cong(X0,X1,X0,X4),true,cyclic(X1,X2,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t39,plain,
cyclic(sk21,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi12,h6,h6,h6]) ).
cnf(t2648,plain,
cyclic(sk21,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t39]) ).
cnf(t2654,plain,
true = ifeq(cong(sk21,sk20,sk20,sk20),true,ifeq(cong(sk21,sk20,sk20,sk20),true,ifeq(true,true,perp(sk20,sk21,sk21,sk20),true),true),true),
inference(cp,[status(thm)],[t270,t2648]) ).
cnf(h19,plain,
coll(sk21,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi1,h5]) ).
cnf(h100,plain,
coll(sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h19,h19]) ).
cnf(h380,plain,
coll(sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h100]) ).
cnf(h65,plain,
para(sk21,sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi63,hi114,h9]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h880,plain,
para(sk21,sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi3,h65]) ).
cnf(h66,plain,
para(sk20,sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi63,h9,hi114]) ).
fof(f5,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD6) ).
fof(f5_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(para(X0,X1,X2,X3),true,ifeq(para(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h886,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi5,h66,h65]) ).
cnf(h18,plain,
coll(sk20,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h5,h5]) ).
cnf(h88,plain,
coll(sk20,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h18]) ).
cnf(h106,plain,
coll(sk20,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi1,h20]) ).
cnf(h546,plain,
coll(sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h106,h88]) ).
fof(f70,axiom,
! [A,B,C,D,M,N] :
( ( midp(N,C,D)
& midp(M,A,B) )
=> eqratio(M,A,A,B,N,C,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD70) ).
fof(f70_nnf,plain,
! [A,B,C,D,M,N] :
( eqratio(M,A,A,B,N,C,C,D)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [M,A,B,N,C,D] :
( eqratio(M,A,A,B,N,C,C,D)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c70,plain,
( eqratio(X4,X0,X0,X1,X5,X2,X2,X3)
| ~ midp(X5,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(hi70,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X3,X4,X5),true,eqratio(X0,X1,X1,X2,X3,X4,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c70]) ).
cnf(h4,plain,
eqratio(sk24,sk21,sk21,sk20,sk24,sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi70,hi114,hi114]) ).
fof(f28,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD29) ).
fof(f28_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( eqratio(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi28,axiom,
ifeq(eqratio(X0,X1,X2,X3,X4,X5,X6,X7),true,eqratio(X0,X1,X4,X5,X2,X3,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(h40,plain,
eqratio(sk24,sk21,sk24,sk21,sk21,sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi28,h4]) ).
fof(f27,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD28) ).
fof(f27_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(P,Q,U,V,A,B,C,D)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(P,Q,U,V,A,B,C,D)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( eqratio(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi27,axiom,
ifeq(eqratio(X0,X1,X2,X3,X4,X5,X6,X7),true,eqratio(X4,X5,X6,X7,X0,X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h363,plain,
eqratio(sk21,sk20,sk21,sk20,sk24,sk21,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi27,h40]) ).
fof(f75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD75) ).
fof(f75_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c75,plain,
( cong(X0,X1,X2,X3)
| ~ cong(X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(hi75,axiom,
ifeq(eqratio(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(cong(X4,X5,X6,X7),true,cong(X0,X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c75]) ).
cnf(h19530,plain,
cong(sk21,sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi75,h363,h860]) ).
cnf(h33011,plain,
midp(sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi67,h19530,h546]) ).
cnf(hi64,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(para(X1,X3,X2,X4),true,ifeq(para(X1,X4,X2,X3),true,midp(X0,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(h33782,plain,
midp(sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi64,h33011,h886,h886]) ).
fof(f45,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD45) ).
fof(f45_nnf,plain,
! [A,B,C,E,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [E,A,B,F,C] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
( midp(X4,X0,X2)
| ~ coll(X4,X0,X2)
| ~ para(X3,X4,X1,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(hi45,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(para(X0,X3,X2,X4),true,ifeq(coll(X3,X1,X4),true,midp(X3,X1,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(h35441,plain,
midp(sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi45,h33782,h880,h380]) ).
fof(f11,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD12) ).
fof(f11_nnf,plain,
! [A,B,C,O] :
( circle(O,A,B,C)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [O,A,B,C] :
( circle(O,A,B,C)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( circle(X3,X0,X1,X2)
| ~ cong(X3,X0,X3,X2)
| ~ cong(X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(cong(X0,X1,X0,X3),true,circle(X0,X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h71,plain,
circle(sk24,sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi11,h6,h6]) ).
fof(f53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD53) ).
fof(f53_nnf,plain,
! [A,B,C,O] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
! [O,A,B,C] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
( perp(X0,X1,X1,X2)
| ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(hi53,axiom,
ifeq(circle(X0,X1,X2,X3),true,ifeq(coll(X0,X1,X3),true,perp(X1,X2,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(h917,plain,
perp(sk21,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi53,h71,h5]) ).
cnf(hi52,axiom,
ifeq(perp(X0,X1,X1,X2),true,ifeq(midp(X3,X0,X2),true,cong(X0,X3,X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(t24,plain,
cong(sk21,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi52,h917,h35441]) ).
cnf(t1012,plain,
cong(sk21,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(t28848,plain,
true = ifeq(true,true,ifeq(cong(sk21,sk20,sk20,sk20),true,ifeq(true,true,perp(sk20,sk21,sk21,sk20),true),true),true),
inference(step,[status(thm)],[t2654,t1012]) ).
cnf(t28849,plain,
true = ifeq(cong(sk21,sk20,sk20,sk20),true,ifeq(true,true,perp(sk20,sk21,sk21,sk20),true),true),
inference(step,[status(thm)],[t28848,t256]) ).
cnf(t28850,plain,
true = ifeq(true,true,ifeq(true,true,perp(sk20,sk21,sk21,sk20),true),true),
inference(step,[status(thm)],[t28849,t1012]) ).
cnf(t28851,plain,
true = ifeq(true,true,perp(sk20,sk21,sk21,sk20),true),
inference(step,[status(thm)],[t28850,t256]) ).
cnf(t28852,plain,
true = perp(sk20,sk21,sk21,sk20),
inference(step,[status(thm)],[t28851,t256]) ).
cnf(t3728,plain,
perp(sk20,sk21,sk21,sk20) = true,
inference(orient,[status(thm)],[t28852]) ).
cnf(t3731,plain,
true = ifeq(true,true,perp(sk21,sk20,sk20,sk21),true),
inference(cp,[status(thm)],[t292,t3728]) ).
cnf(t28862,plain,
true = perp(sk21,sk20,sk20,sk21),
inference(step,[status(thm)],[t3731,t256]) ).
cnf(t3930,plain,
perp(sk21,sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t28862]) ).
cnf(t3938,plain,
true = ifeq(midp(sk20,sk20,sk21),true,ifeq(true,true,cong(sk21,sk20,sk21,sk21),true),true),
inference(cp,[status(thm)],[t323,t3930]) ).
cnf(t6,plain,
midp(sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi45,h33011,h65,h100]) ).
cnf(t1778,plain,
midp(sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t28865,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk20,sk21,sk21),true),true),
inference(step,[status(thm)],[t3938,t1778]) ).
cnf(t28866,plain,
true = ifeq(true,true,cong(sk21,sk20,sk21,sk21),true),
inference(step,[status(thm)],[t28865,t256]) ).
cnf(t28867,plain,
true = cong(sk21,sk20,sk21,sk21),
inference(step,[status(thm)],[t28866,t256]) ).
cnf(t4003,plain,
cong(sk21,sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t28867]) ).
cnf(t4016,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk20,sk21),true,midp(sk21,sk20,sk21),true),true),
inference(cp,[status(thm)],[t272,t4003]) ).
cnf(t28868,plain,
true = ifeq(coll(sk21,sk20,sk21),true,midp(sk21,sk20,sk21),true),
inference(step,[status(thm)],[t4016,t256]) ).
cnf(t98,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t261,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t98]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(t102,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t353,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t102]) ).
cnf(t48,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi5,h66,h65]) ).
cnf(t2231,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t48]) ).
cnf(t2232,plain,
true = ifeq(true,true,coll(sk20,sk21,sk21),true),
inference(cp,[status(thm)],[t353,t2231]) ).
cnf(t28834,plain,
true = coll(sk20,sk21,sk21),
inference(step,[status(thm)],[t2232,t256]) ).
cnf(t3352,plain,
coll(sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t28834]) ).
cnf(t3354,plain,
true = ifeq(true,true,coll(sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t261,t3352]) ).
cnf(t28839,plain,
true = coll(sk21,sk20,sk21),
inference(step,[status(thm)],[t3354,t256]) ).
cnf(t3511,plain,
coll(sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t28839]) ).
cnf(t28869,plain,
true = ifeq(true,true,midp(sk21,sk20,sk21),true),
inference(step,[status(thm)],[t28868,t3511]) ).
cnf(t28870,plain,
true = midp(sk21,sk20,sk21),
inference(step,[status(thm)],[t28869,t256]) ).
cnf(t4041,plain,
midp(sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t28870]) ).
cnf(t26329,plain,
true = ifeq(true,true,midp(sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t26324,t4041]) ).
cnf(t30741,plain,
true = midp(sk21,sk21,sk21),
inference(step,[status(thm)],[t26329,t256]) ).
cnf(t26349,plain,
midp(sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t30741]) ).
cnf(t26357,plain,
true = ifeq(perp(sk21,X1,X1,sk21),true,ifeq(true,true,cong(sk21,sk21,X1,sk21),true),true),
inference(cp,[status(thm)],[t298,t26349]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t61,plain,
eqangle(sk20,sk21,X1,X2,sk20,sk21,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h886]) ).
cnf(t1588,plain,
eqangle(sk20,sk21,X1,X2,sk20,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t61]) ).
cnf(t1593,plain,
true = ifeq(true,true,eqangle(sk20,sk21,sk20,sk21,X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t312,t1588]) ).
cnf(t29266,plain,
true = eqangle(sk20,sk21,sk20,sk21,X1,X2,X1,X2),
inference(step,[status(thm)],[t1593,t256]) ).
cnf(t10583,plain,
eqangle(sk20,sk21,sk20,sk21,X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t29266]) ).
cnf(t10587,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk20,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t306,t10583]) ).
cnf(t29484,plain,
true = eqangle(X1,X2,X1,X2,sk20,sk21,sk20,sk21),
inference(step,[status(thm)],[t10587,t256]) ).
cnf(t12768,plain,
eqangle(X1,X2,X1,X2,sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t29484]) ).
cnf(t12778,plain,
true = ifeq(true,true,ifeq(perp(sk20,sk21,sk20,sk21),true,perp(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t301,t12768]) ).
cnf(t29485,plain,
true = ifeq(perp(sk20,sk21,sk20,sk21),true,perp(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t12778,t256]) ).
cnf(t3729,plain,
true = ifeq(true,true,perp(sk20,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t293,t3728]) ).
cnf(t28861,plain,
true = perp(sk20,sk21,sk20,sk21),
inference(step,[status(thm)],[t3729,t256]) ).
cnf(t3907,plain,
perp(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t28861]) ).
cnf(t29486,plain,
true = ifeq(true,true,perp(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t29485,t3907]) ).
cnf(t29487,plain,
true = perp(X1,X2,X1,X2),
inference(step,[status(thm)],[t29486,t256]) ).
cnf(t12780,plain,
perp(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t29487]) ).
cnf(t12781,plain,
true = ifeq(true,true,perp(X1,X2,X2,X1),true),
inference(cp,[status(thm)],[t293,t12780]) ).
cnf(t29488,plain,
true = perp(X1,X2,X2,X1),
inference(step,[status(thm)],[t12781,t256]) ).
cnf(t12805,plain,
perp(X1,X2,X2,X1) = true,
inference(orient,[status(thm)],[t29488]) ).
cnf(t30745,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk21,X1,sk21),true),true),
inference(step,[status(thm)],[t26357,t12805]) ).
cnf(t30746,plain,
true = ifeq(true,true,cong(sk21,sk21,X1,sk21),true),
inference(step,[status(thm)],[t30745,t256]) ).
cnf(t30747,plain,
true = cong(sk21,sk21,X1,sk21),
inference(step,[status(thm)],[t30746,t256]) ).
cnf(t26400,plain,
cong(sk21,sk21,X1,sk21) = true,
inference(orient,[status(thm)],[t30747]) ).
cnf(t26403,plain,
true = ifeq(true,true,cong(sk21,sk21,sk21,X1),true),
inference(cp,[status(thm)],[t268,t26400]) ).
cnf(t30751,plain,
true = cong(sk21,sk21,sk21,X1),
inference(step,[status(thm)],[t26403,t256]) ).
cnf(t26509,plain,
cong(sk21,sk21,sk21,X1) = true,
inference(orient,[status(thm)],[t30751]) ).
cnf(t26512,plain,
true = ifeq(true,true,eqangle(sk21,sk21,sk21,X1,sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t282,t26509]) ).
cnf(t30810,plain,
true = eqangle(sk21,sk21,sk21,X1,sk21,X1,sk21,X1),
inference(step,[status(thm)],[t26512,t256]) ).
cnf(t26911,plain,
eqangle(sk21,sk21,sk21,X1,sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t30810]) ).
cnf(t26922,plain,
true = ifeq(true,true,ifeq(perp(sk21,X1,sk21,X1),true,perp(sk21,sk21,sk21,X1),true),true),
inference(cp,[status(thm)],[t301,t26911]) ).
cnf(t30812,plain,
true = ifeq(perp(sk21,X1,sk21,X1),true,perp(sk21,sk21,sk21,X1),true),
inference(step,[status(thm)],[t26922,t256]) ).
cnf(t30813,plain,
true = ifeq(true,true,perp(sk21,sk21,sk21,X1),true),
inference(step,[status(thm)],[t30812,t12780]) ).
cnf(t30814,plain,
true = perp(sk21,sk21,sk21,X1),
inference(step,[status(thm)],[t30813,t256]) ).
cnf(t26936,plain,
perp(sk21,sk21,sk21,X1) = true,
inference(orient,[status(thm)],[t30814]) ).
cnf(t26937,plain,
true = ifeq(true,true,perp(sk21,sk21,X1,sk21),true),
inference(cp,[status(thm)],[t293,t26936]) ).
cnf(t30817,plain,
true = perp(sk21,sk21,X1,sk21),
inference(step,[status(thm)],[t26937,t256]) ).
cnf(t26982,plain,
perp(sk21,sk21,X1,sk21) = true,
inference(orient,[status(thm)],[t30817]) ).
cnf(t26983,plain,
true = ifeq(true,true,perp(X1,sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t292,t26982]) ).
cnf(t30820,plain,
true = perp(X1,sk21,sk21,sk21),
inference(step,[status(thm)],[t26983,t256]) ).
cnf(t27029,plain,
perp(X1,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t30820]) ).
cnf(t27034,plain,
true = ifeq(midp(sk21,sk21,sk21),true,ifeq(true,true,cong(X1,sk21,X1,sk21),true),true),
inference(cp,[status(thm)],[t323,t27029]) ).
cnf(t30821,plain,
true = ifeq(true,true,ifeq(true,true,cong(X1,sk21,X1,sk21),true),true),
inference(step,[status(thm)],[t27034,t26349]) ).
cnf(t30822,plain,
true = ifeq(true,true,cong(X1,sk21,X1,sk21),true),
inference(step,[status(thm)],[t30821,t256]) ).
cnf(t30823,plain,
true = cong(X1,sk21,X1,sk21),
inference(step,[status(thm)],[t30822,t256]) ).
cnf(t27050,plain,
cong(X1,sk21,X1,sk21) = true,
inference(orient,[status(thm)],[t30823]) ).
cnf(t27054,plain,
true = ifeq(true,true,cong(X1,sk21,sk21,X1),true),
inference(cp,[status(thm)],[t268,t27050]) ).
cnf(t30824,plain,
true = cong(X1,sk21,sk21,X1),
inference(step,[status(thm)],[t27054,t256]) ).
cnf(t27076,plain,
cong(X1,sk21,sk21,X1) = true,
inference(orient,[status(thm)],[t30824]) ).
cnf(t27079,plain,
true = ifeq(true,true,cong(sk21,X1,X1,sk21),true),
inference(cp,[status(thm)],[t266,t27076]) ).
cnf(t30825,plain,
true = cong(sk21,X1,X1,sk21),
inference(step,[status(thm)],[t27079,t256]) ).
cnf(t27093,plain,
cong(sk21,X1,X1,sk21) = true,
inference(orient,[status(thm)],[t30825]) ).
cnf(t27096,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t268,t27093]) ).
cnf(t30826,plain,
true = cong(sk21,X1,sk21,X1),
inference(step,[status(thm)],[t27096,t256]) ).
cnf(t27109,plain,
cong(sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t30826]) ).
cnf(t27120,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t27109]) ).
cnf(t30827,plain,
true = ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t27120,t256]) ).
cnf(t30828,plain,
true = ifeq(true,true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t30827,t27109]) ).
cnf(t30829,plain,
true = perp(sk21,sk21,X2,X1),
inference(step,[status(thm)],[t30828,t256]) ).
cnf(t27134,plain,
perp(sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t30829]) ).
cnf(t27135,plain,
true = ifeq(true,true,perp(X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t292,t27134]) ).
cnf(t30830,plain,
true = perp(X1,X2,sk21,sk21),
inference(step,[status(thm)],[t27135,t256]) ).
cnf(t27154,plain,
perp(X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t30830]) ).
cnf(t27160,plain,
true = ifeq(true,true,ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t27154]) ).
cnf(t30831,plain,
true = ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t27160,t256]) ).
cnf(t30832,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t30831,t27134]) ).
cnf(t30833,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t30832,t256]) ).
cnf(t27175,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t30833]) ).
cnf(t30834,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t346,t27175]) ).
cnf(t30835,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t30834,t256]) ).
cnf(t27176,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t30835]) ).
cnf(t27890,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t27176]) ).
cnf(t27892,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t312,t27890]) ).
cnf(t30957,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t27892,t256]) ).
cnf(t28236,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t30957]) ).
cnf(t28238,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t306,t28236]) ).
cnf(t31014,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t28238,t256]) ).
cnf(t28505,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t31014]) ).
cnf(t28510,plain,
true = ifeq(eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(cp,[status(thm)],[t304,t28505]) ).
cnf(t31050,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t28510,t28236]) ).
cnf(t31051,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t31050,t256]) ).
cnf(t31052,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t31051,t256]) ).
cnf(t28824,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t31052]) ).
cnf(c117,plain,
~ eqangle(sk20,sk22,sk22,sk25,sk25,sk22,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk20,sk22,sk22,sk25,sk25,sk22,sk22,sk21) != true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t28824]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO597+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.57 % Computer : n004.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Wed Sep 23 12:31:06 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 182.71/23.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 182.71/23.88 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------