%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO656+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:18:24 PM UTC 2026
% Result : Theorem 193.49s 27.95s
% Output : Proof 193.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 33
% Syntax : Number of formulae : 326 ( 198 unt; 0 def)
% Number of atoms : 534 ( 195 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 361 ( 153 ~; 147 |; 28 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 986 ( 48 sgn 471 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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(t184,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)],[t184]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/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(t118,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)],[t118]) ).
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/sandbox2/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(t171,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)],[t171]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/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(t110,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)],[t110]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox2/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(t111,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)],[t111]) ).
fof(f55,axiom,
! [A,B,M,O] :
( ( perp(O,M,A,B)
& midp(M,A,B) )
=> cong(O,A,O,B) ),
file('/export/starexec/sandbox2/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(t168,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)],[t168]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox2/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(t117,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)],[t117]) ).
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/sandbox2/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/sandbox2/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(t138,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)],[t138]) ).
fof(f52,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('/export/starexec/sandbox2/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(t169,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)],[t169]) ).
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/sandbox2/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/sandbox2/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,D,E,F] :
( ( eqangle(F,D,D,B,F,D,D,C)
& eqangle(E,D,D,A,E,D,D,C)
& midp(D,B,A) )
=> para(E,F,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULLmoreE02314) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F] :
( ( eqangle(F,D,D,B,F,D,D,C)
& eqangle(E,D,D,A,E,D,D,C)
& midp(D,B,A) )
=> para(E,F,A,B) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F] :
( ~ para(E,F,A,B)
& eqangle(F,D,D,B,F,D,D,C)
& eqangle(E,D,D,A,E,D,D,C)
& midp(D,B,A) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk24,sk25,sk20,sk21)
& eqangle(sk25,sk23,sk23,sk21,sk25,sk23,sk23,sk22)
& eqangle(sk24,sk23,sk23,sk20,sk24,sk23,sk23,sk22)
& midp(sk23,sk21,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25])],[f94_nnf]) ).
cnf(c113,plain,
midp(sk23,sk21,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
midp(sk23,sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h4,plain,
coll(sk23,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi69,hi113]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/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(h38,plain,
coll(sk20,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h4,h4]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/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(h84,plain,
coll(sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h38]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/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(h132,plain,
coll(sk23,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi1,h84]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/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(h5,plain,
cong(sk23,sk21,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi113]) ).
cnf(hi23,axiom,
ifeq(cong(X0,X1,X2,X3),true,cong(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h45,plain,
cong(sk23,sk20,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi23,h5]) ).
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/sandbox2/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(h373,plain,
cong(sk23,sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi24,h45,h5]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/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(h6382,plain,
midp(sk23,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi67,h373,h132]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox2/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(t46,plain,
para(sk21,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi63,hi113,h6382]) ).
cnf(t2425,plain,
para(sk21,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t46]) ).
cnf(t2442,plain,
true = ifeq(midp(X1,sk21,sk20),true,ifeq(true,true,ifeq(para(sk21,sk20,sk20,sk20),true,midp(X1,sk20,sk20),true),true),true),
inference(cp,[status(thm)],[t333,t2425]) ).
cnf(t40,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t40]) ).
cnf(t41845,plain,
true = ifeq(midp(X1,sk21,sk20),true,ifeq(para(sk21,sk20,sk20,sk20),true,midp(X1,sk20,sk20),true),true),
inference(step,[status(thm)],[t2442,t256]) ).
cnf(t41846,plain,
true = ifeq(midp(X1,sk21,sk20),true,ifeq(true,true,midp(X1,sk20,sk20),true),true),
inference(step,[status(thm)],[t41845,t2425]) ).
cnf(t41847,plain,
true = ifeq(midp(X1,sk21,sk20),true,midp(X1,sk20,sk20),true),
inference(step,[status(thm)],[t41846,t256]) ).
cnf(t38212,plain,
ifeq(midp(X1,sk21,sk20),true,midp(X1,sk20,sk20),true) = true,
inference(orient,[status(thm)],[t41847]) ).
cnf(h40,plain,
coll(sk23,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4]) ).
cnf(h105,plain,
coll(sk21,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h40,h40]) ).
cnf(h288,plain,
coll(sk21,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h105]) ).
cnf(h543,plain,
coll(sk23,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi1,h288]) ).
cnf(h372,plain,
cong(sk23,sk21,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi24,h5,h45]) ).
cnf(h5986,plain,
midp(sk23,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi67,h372,h543]) ).
cnf(t52,plain,
para(sk21,sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi63,h5986,hi113]) ).
cnf(t2581,plain,
para(sk21,sk21,sk21,sk20) = true,
inference(orient,[status(thm)],[t52]) ).
cnf(t2599,plain,
true = ifeq(midp(X1,sk21,sk21),true,ifeq(true,true,ifeq(para(sk21,sk20,sk21,sk21),true,midp(X1,sk21,sk20),true),true),true),
inference(cp,[status(thm)],[t333,t2581]) ).
cnf(t41854,plain,
true = ifeq(midp(X1,sk21,sk21),true,ifeq(para(sk21,sk20,sk21,sk21),true,midp(X1,sk21,sk20),true),true),
inference(step,[status(thm)],[t2599,t256]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/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(h8,plain,
midp(sk23,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi113]) ).
cnf(t49,plain,
para(sk21,sk20,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi63,h5986,h8]) ).
cnf(t2501,plain,
para(sk21,sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(t41855,plain,
true = ifeq(midp(X1,sk21,sk21),true,ifeq(true,true,midp(X1,sk21,sk20),true),true),
inference(step,[status(thm)],[t41854,t2501]) ).
cnf(t41856,plain,
true = ifeq(midp(X1,sk21,sk21),true,midp(X1,sk21,sk20),true),
inference(step,[status(thm)],[t41855,t256]) ).
cnf(t38229,plain,
ifeq(midp(X1,sk21,sk21),true,midp(X1,sk21,sk20),true) = true,
inference(orient,[status(thm)],[t41856]) ).
cnf(t162,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)],[t162]) ).
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/sandbox2/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(h3,plain,
eqratio(sk23,sk21,sk21,sk20,sk23,sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi70,hi113,hi113]) ).
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/sandbox2/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(h41,plain,
eqratio(sk23,sk21,sk23,sk21,sk21,sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi28,h3]) ).
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/sandbox2/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(h362,plain,
eqratio(sk21,sk20,sk21,sk20,sk23,sk21,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi27,h41]) ).
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/sandbox2/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(t20,plain,
cong(sk21,sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi75,h362,h372]) ).
cnf(t903,plain,
cong(sk21,sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t907,plain,
true = ifeq(true,true,cong(sk21,sk20,sk20,sk21),true),
inference(cp,[status(thm)],[t268,t903]) ).
cnf(t38783,plain,
true = cong(sk21,sk20,sk20,sk21),
inference(step,[status(thm)],[t907,t256]) ).
cnf(t3672,plain,
cong(sk21,sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t38783]) ).
cnf(t3674,plain,
true = ifeq(true,true,cong(sk20,sk21,sk21,sk20),true),
inference(cp,[status(thm)],[t266,t3672]) ).
cnf(t38796,plain,
true = cong(sk20,sk21,sk21,sk20),
inference(step,[status(thm)],[t3674,t256]) ).
cnf(t3859,plain,
cong(sk20,sk21,sk21,sk20) = true,
inference(orient,[status(thm)],[t38796]) ).
cnf(t3861,plain,
true = ifeq(true,true,cong(sk20,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t268,t3859]) ).
cnf(t38801,plain,
true = cong(sk20,sk21,sk20,sk21),
inference(step,[status(thm)],[t3861,t256]) ).
cnf(t3968,plain,
cong(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t38801]) ).
cnf(t3980,plain,
true = ifeq(true,true,ifeq(coll(sk20,sk21,sk21),true,midp(sk20,sk21,sk21),true),true),
inference(cp,[status(thm)],[t272,t3968]) ).
cnf(t38802,plain,
true = ifeq(coll(sk20,sk21,sk21),true,midp(sk20,sk21,sk21),true),
inference(step,[status(thm)],[t3980,t256]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/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(t109,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)],[t109]) ).
cnf(h71,plain,
para(sk21,sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi63,hi113,h8]) ).
cnf(h72,plain,
para(sk20,sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi63,h8,hi113]) ).
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/sandbox2/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(t43,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi5,h72,h71]) ).
cnf(t2346,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t43]) ).
cnf(t2347,plain,
true = ifeq(true,true,coll(sk20,sk21,sk21),true),
inference(cp,[status(thm)],[t353,t2346]) ).
cnf(t38769,plain,
true = coll(sk20,sk21,sk21),
inference(step,[status(thm)],[t2347,t256]) ).
cnf(t3307,plain,
coll(sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t38769]) ).
cnf(t38803,plain,
true = ifeq(true,true,midp(sk20,sk21,sk21),true),
inference(step,[status(thm)],[t38802,t3307]) ).
cnf(t38804,plain,
true = midp(sk20,sk21,sk21),
inference(step,[status(thm)],[t38803,t256]) ).
cnf(t4009,plain,
midp(sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t38804]) ).
cnf(t38230,plain,
true = ifeq(true,true,midp(sk20,sk21,sk20),true),
inference(cp,[status(thm)],[t38229,t4009]) ).
cnf(t41857,plain,
true = midp(sk20,sk21,sk20),
inference(step,[status(thm)],[t38230,t256]) ).
cnf(t38238,plain,
midp(sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t41857]) ).
cnf(t38239,plain,
true = ifeq(true,true,midp(sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t38212,t38238]) ).
cnf(t41858,plain,
true = midp(sk20,sk20,sk20),
inference(step,[status(thm)],[t38239,t256]) ).
cnf(t38257,plain,
midp(sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t41858]) ).
cnf(t38265,plain,
true = ifeq(perp(sk20,X1,X1,sk20),true,ifeq(true,true,cong(sk20,sk20,X1,sk20),true),true),
inference(cp,[status(thm)],[t298,t38257]) ).
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/sandbox2/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(t177,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)],[t177]) ).
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/sandbox2/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(t174,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)],[t174]) ).
cnf(h1014,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi5,h72,h71]) ).
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/sandbox2/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(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(t69,plain,
eqangle(sk20,sk21,X1,X2,sk20,sk21,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h1014]) ).
cnf(t1675,plain,
eqangle(sk20,sk21,X1,X2,sk20,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t69]) ).
cnf(t1680,plain,
true = ifeq(true,true,eqangle(sk20,sk21,sk20,sk21,X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t312,t1675]) ).
cnf(t38997,plain,
true = eqangle(sk20,sk21,sk20,sk21,X1,X2,X1,X2),
inference(step,[status(thm)],[t1680,t256]) ).
cnf(t6609,plain,
eqangle(sk20,sk21,sk20,sk21,X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t38997]) ).
cnf(t6613,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk20,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t306,t6609]) ).
cnf(t39193,plain,
true = eqangle(X1,X2,X1,X2,sk20,sk21,sk20,sk21),
inference(step,[status(thm)],[t6613,t256]) ).
cnf(t8650,plain,
eqangle(X1,X2,X1,X2,sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t39193]) ).
cnf(t8660,plain,
true = ifeq(true,true,ifeq(perp(sk20,sk21,sk20,sk21),true,perp(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t301,t8650]) ).
cnf(t39194,plain,
true = ifeq(perp(sk20,sk21,sk20,sk21),true,perp(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t8660,t256]) ).
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/sandbox2/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/sandbox2/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(t37,plain,
cyclic(sk21,sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi12,h372,h5,h5]) ).
cnf(t2827,plain,
cyclic(sk21,sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t37]) ).
cnf(t2834,plain,
true = ifeq(cong(sk21,sk20,sk21,sk20),true,ifeq(cong(sk21,sk20,sk21,sk20),true,ifeq(true,true,perp(sk20,sk21,sk21,sk20),true),true),true),
inference(cp,[status(thm)],[t270,t2827]) ).
cnf(t38788,plain,
true = ifeq(true,true,ifeq(cong(sk21,sk20,sk21,sk20),true,ifeq(true,true,perp(sk20,sk21,sk21,sk20),true),true),true),
inference(step,[status(thm)],[t2834,t903]) ).
cnf(t38789,plain,
true = ifeq(cong(sk21,sk20,sk21,sk20),true,ifeq(true,true,perp(sk20,sk21,sk21,sk20),true),true),
inference(step,[status(thm)],[t38788,t256]) ).
cnf(t38790,plain,
true = ifeq(true,true,ifeq(true,true,perp(sk20,sk21,sk21,sk20),true),true),
inference(step,[status(thm)],[t38789,t903]) ).
cnf(t38791,plain,
true = ifeq(true,true,perp(sk20,sk21,sk21,sk20),true),
inference(step,[status(thm)],[t38790,t256]) ).
cnf(t38792,plain,
true = perp(sk20,sk21,sk21,sk20),
inference(step,[status(thm)],[t38791,t256]) ).
cnf(t3774,plain,
perp(sk20,sk21,sk21,sk20) = true,
inference(orient,[status(thm)],[t38792]) ).
cnf(t3775,plain,
true = ifeq(true,true,perp(sk20,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t293,t3774]) ).
cnf(t38798,plain,
true = perp(sk20,sk21,sk20,sk21),
inference(step,[status(thm)],[t3775,t256]) ).
cnf(t3895,plain,
perp(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t38798]) ).
cnf(t39195,plain,
true = ifeq(true,true,perp(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t39194,t3895]) ).
cnf(t39196,plain,
true = perp(X1,X2,X1,X2),
inference(step,[status(thm)],[t39195,t256]) ).
cnf(t8662,plain,
perp(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t39196]) ).
cnf(t8663,plain,
true = ifeq(true,true,perp(X1,X2,X2,X1),true),
inference(cp,[status(thm)],[t293,t8662]) ).
cnf(t39197,plain,
true = perp(X1,X2,X2,X1),
inference(step,[status(thm)],[t8663,t256]) ).
cnf(t8687,plain,
perp(X1,X2,X2,X1) = true,
inference(orient,[status(thm)],[t39197]) ).
cnf(t41860,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk20,sk20,X1,sk20),true),true),
inference(step,[status(thm)],[t38265,t8687]) ).
cnf(t41861,plain,
true = ifeq(true,true,cong(sk20,sk20,X1,sk20),true),
inference(step,[status(thm)],[t41860,t256]) ).
cnf(t41862,plain,
true = cong(sk20,sk20,X1,sk20),
inference(step,[status(thm)],[t41861,t256]) ).
cnf(t38292,plain,
cong(sk20,sk20,X1,sk20) = true,
inference(orient,[status(thm)],[t41862]) ).
cnf(t38297,plain,
true = ifeq(true,true,cong(sk20,sk20,sk20,X1),true),
inference(cp,[status(thm)],[t268,t38292]) ).
cnf(t41863,plain,
true = cong(sk20,sk20,sk20,X1),
inference(step,[status(thm)],[t38297,t256]) ).
cnf(t38324,plain,
cong(sk20,sk20,sk20,X1) = true,
inference(orient,[status(thm)],[t41863]) ).
cnf(t38331,plain,
true = ifeq(true,true,eqangle(sk20,sk20,sk20,X1,sk20,X1,sk20,X1),true),
inference(cp,[status(thm)],[t282,t38324]) ).
cnf(t41873,plain,
true = eqangle(sk20,sk20,sk20,X1,sk20,X1,sk20,X1),
inference(step,[status(thm)],[t38331,t256]) ).
cnf(t38484,plain,
eqangle(sk20,sk20,sk20,X1,sk20,X1,sk20,X1) = true,
inference(orient,[status(thm)],[t41873]) ).
cnf(t38495,plain,
true = ifeq(true,true,ifeq(perp(sk20,X1,sk20,X1),true,perp(sk20,sk20,sk20,X1),true),true),
inference(cp,[status(thm)],[t301,t38484]) ).
cnf(t41875,plain,
true = ifeq(perp(sk20,X1,sk20,X1),true,perp(sk20,sk20,sk20,X1),true),
inference(step,[status(thm)],[t38495,t256]) ).
cnf(t41876,plain,
true = ifeq(true,true,perp(sk20,sk20,sk20,X1),true),
inference(step,[status(thm)],[t41875,t8662]) ).
cnf(t41877,plain,
true = perp(sk20,sk20,sk20,X1),
inference(step,[status(thm)],[t41876,t256]) ).
cnf(t38509,plain,
perp(sk20,sk20,sk20,X1) = true,
inference(orient,[status(thm)],[t41877]) ).
cnf(t38510,plain,
true = ifeq(true,true,perp(sk20,sk20,X1,sk20),true),
inference(cp,[status(thm)],[t293,t38509]) ).
cnf(t41880,plain,
true = perp(sk20,sk20,X1,sk20),
inference(step,[status(thm)],[t38510,t256]) ).
cnf(t38555,plain,
perp(sk20,sk20,X1,sk20) = true,
inference(orient,[status(thm)],[t41880]) ).
cnf(t38556,plain,
true = ifeq(true,true,perp(X1,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t292,t38555]) ).
cnf(t41883,plain,
true = perp(X1,sk20,sk20,sk20),
inference(step,[status(thm)],[t38556,t256]) ).
cnf(t38597,plain,
perp(X1,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t41883]) ).
cnf(t38600,plain,
true = ifeq(midp(sk20,sk20,sk20),true,ifeq(true,true,cong(X1,sk20,X1,sk20),true),true),
inference(cp,[status(thm)],[t323,t38597]) ).
cnf(t41884,plain,
true = ifeq(true,true,ifeq(true,true,cong(X1,sk20,X1,sk20),true),true),
inference(step,[status(thm)],[t38600,t38257]) ).
cnf(t41885,plain,
true = ifeq(true,true,cong(X1,sk20,X1,sk20),true),
inference(step,[status(thm)],[t41884,t256]) ).
cnf(t41886,plain,
true = cong(X1,sk20,X1,sk20),
inference(step,[status(thm)],[t41885,t256]) ).
cnf(t38616,plain,
cong(X1,sk20,X1,sk20) = true,
inference(orient,[status(thm)],[t41886]) ).
cnf(t38622,plain,
true = ifeq(true,true,cong(X1,sk20,sk20,X1),true),
inference(cp,[status(thm)],[t268,t38616]) ).
cnf(t41887,plain,
true = cong(X1,sk20,sk20,X1),
inference(step,[status(thm)],[t38622,t256]) ).
cnf(t38649,plain,
cong(X1,sk20,sk20,X1) = true,
inference(orient,[status(thm)],[t41887]) ).
cnf(t38654,plain,
true = ifeq(true,true,cong(sk20,X1,X1,sk20),true),
inference(cp,[status(thm)],[t266,t38649]) ).
cnf(t41888,plain,
true = cong(sk20,X1,X1,sk20),
inference(step,[status(thm)],[t38654,t256]) ).
cnf(t38669,plain,
cong(sk20,X1,X1,sk20) = true,
inference(orient,[status(thm)],[t41888]) ).
cnf(t38674,plain,
true = ifeq(true,true,cong(sk20,X1,sk20,X1),true),
inference(cp,[status(thm)],[t268,t38669]) ).
cnf(t41889,plain,
true = cong(sk20,X1,sk20,X1),
inference(step,[status(thm)],[t38674,t256]) ).
cnf(t38688,plain,
cong(sk20,X1,sk20,X1) = true,
inference(orient,[status(thm)],[t41889]) ).
cnf(t38703,plain,
true = ifeq(true,true,ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t38688]) ).
cnf(t41890,plain,
true = ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t38703,t256]) ).
cnf(t41891,plain,
true = ifeq(true,true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t41890,t38688]) ).
cnf(t41892,plain,
true = perp(sk20,sk20,X2,X1),
inference(step,[status(thm)],[t41891,t256]) ).
cnf(t38717,plain,
perp(sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t41892]) ).
cnf(t38718,plain,
true = ifeq(true,true,perp(X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t292,t38717]) ).
cnf(t41893,plain,
true = perp(X1,X2,sk20,sk20),
inference(step,[status(thm)],[t38718,t256]) ).
cnf(t38737,plain,
perp(X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t41893]) ).
cnf(t38741,plain,
true = ifeq(true,true,ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t38737]) ).
cnf(t41894,plain,
true = ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t38741,t256]) ).
cnf(t41895,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t41894,t38717]) ).
cnf(t41896,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t41895,t256]) ).
cnf(t38756,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t41896]) ).
cnf(c116,plain,
~ para(sk24,sk25,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk24,sk25,sk20,sk21) != true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t38756]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO656+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 12:40:50 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 193.49/27.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 193.49/27.95 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------