%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO581+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 : n017.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 01:18:12 PM UTC 2026
% Result : Theorem 201.79s 26.09s
% Output : Proof 201.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 78
% Number of leaves : 26
% Syntax : Number of formulae : 285 ( 184 unt; 0 def)
% Number of atoms : 460 ( 179 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 291 ( 116 ~; 110 |; 39 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 965 ( 108 sgn 372 !; 10 ?)
% 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(t182,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)],[t182]) ).
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(t179,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)],[t179]) ).
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(t156,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)],[t156]) ).
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(t189,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)],[t189]) ).
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(t134,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)],[t134]) ).
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(t176,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)],[t176]) ).
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(t115,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t336,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t115]) ).
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(f38,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD39) ).
fof(f38_nnf,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,P,Q,C,D] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t155,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t314,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t155]) ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD19) ).
fof(f18_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t181,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t308,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(orient,[status(thm)],[t181]) ).
fof(f85,axiom,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,H,A,C)
& perp(A,H,B,C) )
=> ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX10) ).
fof(f85_nnf,plain,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(nnf_transformation,[status(thm)],[f85]) ).
fof(f85_sk,plain,
! [A,H,B,C] :
( ( perp(B,sk10(A,B,C,H),C,A)
& coll(sk10(A,B,C,H),C,A)
& perp(A,sk9(A,B,C,H),C,B)
& coll(sk9(A,B,C,H),C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f85_nnf]) ).
cnf(c97,plain,
( coll(sk10(X0,X1,X2,X3),X2,X0)
| ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(hi97,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X1,X0,X3),true,coll(sk10(X0,X2,X3,X1),X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c97]) ).
fof(f94,conjecture,
! [A,B,C,F,E,P] :
( ( coll(P,A,F)
& coll(P,B,E)
& cong(A,E,E,F)
& eqangle(B,A,A,E,A,E,E,F)
& perp(C,A,C,B) )
=> eqangle(A,C,C,P,P,C,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416043) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,F,E,P] :
( ( coll(P,A,F)
& coll(P,B,E)
& cong(A,E,E,F)
& eqangle(B,A,A,E,A,E,E,F)
& perp(C,A,C,B) )
=> eqangle(A,C,C,P,P,C,C,B) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,F,E,P] :
( ~ eqangle(A,C,C,P,P,C,C,B)
& coll(P,A,F)
& coll(P,B,E)
& cong(A,E,E,F)
& eqangle(B,A,A,E,A,E,E,F)
& perp(C,A,C,B) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk20,sk22,sk22,sk25,sk25,sk22,sk22,sk21)
& coll(sk25,sk20,sk23)
& coll(sk25,sk21,sk24)
& cong(sk20,sk24,sk24,sk23)
& eqangle(sk21,sk20,sk20,sk24,sk20,sk24,sk24,sk23)
& perp(sk22,sk20,sk22,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25])],[f94_nnf]) ).
cnf(c113,plain,
perp(sk22,sk20,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
perp(sk22,sk20,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h1,plain,
coll(sk10(sk22,sk22,sk21,sk20),sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi97,hi113,hi113]) ).
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(h22,plain,
coll(sk21,sk10(sk22,sk22,sk21,sk20),sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,h1]) ).
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(h83,plain,
coll(sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h22,h22]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h4,plain,
perp(sk22,sk21,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi113]) ).
cnf(hi8,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h35,plain,
para(sk22,sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi113,h4]) ).
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(h128,plain,
eqangle(sk22,sk20,V0,V1,sk22,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h35]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(h540,plain,
cyclic(sk20,sk21,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h128,h83]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD41) ).
fof(f40_nnf,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(hi40,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,eqangle(X2,X0,X2,X1,X3,X0,X3,X1),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t58,plain,
eqangle(sk22,sk20,sk22,sk21,sk22,sk20,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi40,h540]) ).
cnf(t1733,plain,
eqangle(sk22,sk20,sk22,sk21,sk22,sk20,sk22,sk21) = true,
inference(orient,[status(thm)],[t58]) ).
cnf(t1736,plain,
true = ifeq(true,true,para(sk22,sk20,sk22,sk20),true),
inference(cp,[status(thm)],[t314,t1733]) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t23]) ).
cnf(t56463,plain,
true = para(sk22,sk20,sk22,sk20),
inference(step,[status(thm)],[t1736,t256]) ).
cnf(t3682,plain,
para(sk22,sk20,sk22,sk20) = true,
inference(orient,[status(thm)],[t56463]) ).
cnf(t3686,plain,
true = ifeq(true,true,eqangle(sk22,sk20,X1,X2,sk22,sk20,X1,X2),true),
inference(cp,[status(thm)],[t346,t3682]) ).
cnf(t56853,plain,
true = eqangle(sk22,sk20,X1,X2,sk22,sk20,X1,X2),
inference(step,[status(thm)],[t3686,t256]) ).
cnf(t11360,plain,
eqangle(sk22,sk20,X1,X2,sk22,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t56853]) ).
cnf(t11366,plain,
true = ifeq(true,true,eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20),true),
inference(cp,[status(thm)],[t308,t11360]) ).
cnf(t57659,plain,
true = eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20),
inference(step,[status(thm)],[t11366,t256]) ).
cnf(t25439,plain,
eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20) = true,
inference(orient,[status(thm)],[t57659]) ).
cnf(t25441,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t25439]) ).
cnf(t57660,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t25441,t256]) ).
cnf(t25463,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t57660]) ).
cnf(t25480,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),true),
inference(cp,[status(thm)],[t333,t25463]) ).
cnf(t60517,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t25480,t256]) ).
cnf(t60518,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t60517,t25463]) ).
cnf(t60519,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t60518,t256]) ).
cnf(t54680,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t60519]) ).
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(t161,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)],[t161]) ).
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(t126,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)],[t126]) ).
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(t127,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)],[t127]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t253,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t357,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
cnf(t154,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t359,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t154]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD15) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t129,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t362,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t129]) ).
cnf(c116,plain,
coll(sk25,sk21,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk25,sk21,sk24) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h12,plain,
coll(sk21,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi116]) ).
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(h30,plain,
coll(sk21,sk24,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h12]) ).
cnf(h89,plain,
coll(sk25,sk25,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h30,h30]) ).
cnf(c117,plain,
coll(sk25,sk20,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk25,sk20,sk23) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h15,plain,
coll(sk20,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi117]) ).
cnf(h59,plain,
coll(sk20,sk23,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi0,h15]) ).
cnf(h165,plain,
coll(sk25,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h59,h59]) ).
cnf(h579,plain,
coll(sk20,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h165,h89]) ).
cnf(h1367,plain,
coll(sk20,sk25,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h579]) ).
cnf(h2815,plain,
coll(sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1367,h1367]) ).
cnf(c98,plain,
( perp(X1,sk10(X0,X1,X2,X3),X2,X0)
| ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(hi98,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X1,X0,X3),true,perp(X2,sk10(X0,X2,X3,X1),X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c98]) ).
cnf(h0,plain,
perp(sk22,sk10(sk22,sk22,sk21,sk20),sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi98,hi113,hi113]) ).
cnf(h17,plain,
perp(sk21,sk22,sk22,sk10(sk22,sk22,sk21,sk20)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
cnf(h68,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,h17,h0]) ).
cnf(h239,plain,
eqangle(sk21,sk22,V0,V1,sk21,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h68]) ).
cnf(t21,plain,
cyclic(sk22,sk20,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h239,h2815]) ).
cnf(t2652,plain,
cyclic(sk22,sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t2653,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk20,sk21),true),
inference(cp,[status(thm)],[t362,t2652]) ).
cnf(t56477,plain,
true = cyclic(sk22,sk21,sk20,sk21),
inference(step,[status(thm)],[t2653,t256]) ).
cnf(t4100,plain,
cyclic(sk22,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t56477]) ).
cnf(t4105,plain,
true = ifeq(true,true,eqangle(sk20,sk22,sk20,sk21,sk21,sk22,sk21,sk21),true),
inference(cp,[status(thm)],[t359,t4100]) ).
cnf(t56858,plain,
true = eqangle(sk20,sk22,sk20,sk21,sk21,sk22,sk21,sk21),
inference(step,[status(thm)],[t4105,t256]) ).
cnf(t11457,plain,
eqangle(sk20,sk22,sk20,sk21,sk21,sk22,sk21,sk21) = true,
inference(orient,[status(thm)],[t56858]) ).
cnf(t11473,plain,
true = ifeq(cyclic(sk22,sk21,sk20,sk22),true,ifeq(cyclic(sk22,sk21,sk20,sk21),true,ifeq(cyclic(sk22,sk21,sk20,sk21),true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),true),true),
inference(cp,[status(thm)],[t357,t11457]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t130,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t360,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t130]) ).
cnf(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t15,plain,
cyclic(sk20,sk22,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi14,h540]) ).
cnf(t2690,plain,
cyclic(sk20,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t2695,plain,
true = ifeq(true,true,cyclic(sk22,sk20,sk21,sk22),true),
inference(cp,[status(thm)],[t360,t2690]) ).
cnf(t56482,plain,
true = cyclic(sk22,sk20,sk21,sk22),
inference(step,[status(thm)],[t2695,t256]) ).
cnf(t4187,plain,
cyclic(sk22,sk20,sk21,sk22) = true,
inference(orient,[status(thm)],[t56482]) ).
cnf(t4190,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk20,sk22),true),
inference(cp,[status(thm)],[t362,t4187]) ).
cnf(t56508,plain,
true = cyclic(sk22,sk21,sk20,sk22),
inference(step,[status(thm)],[t4190,t256]) ).
cnf(t4702,plain,
cyclic(sk22,sk21,sk20,sk22) = true,
inference(orient,[status(thm)],[t56508]) ).
cnf(t56859,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk21,sk20,sk21),true,ifeq(cyclic(sk22,sk21,sk20,sk21),true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),true),true),
inference(step,[status(thm)],[t11473,t4702]) ).
cnf(t56860,plain,
true = ifeq(cyclic(sk22,sk21,sk20,sk21),true,ifeq(cyclic(sk22,sk21,sk20,sk21),true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),true),
inference(step,[status(thm)],[t56859,t256]) ).
cnf(t56861,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk21,sk20,sk21),true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),true),
inference(step,[status(thm)],[t56860,t4100]) ).
cnf(t56862,plain,
true = ifeq(cyclic(sk22,sk21,sk20,sk21),true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),
inference(step,[status(thm)],[t56861,t256]) ).
cnf(t56863,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),true),
inference(step,[status(thm)],[t56862,t4100]) ).
cnf(t56864,plain,
true = ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),
inference(step,[status(thm)],[t56863,t256]) ).
cnf(t56865,plain,
true = cong(sk22,sk21,sk22,sk21),
inference(step,[status(thm)],[t56864,t256]) ).
cnf(t11474,plain,
cong(sk22,sk21,sk22,sk21) = true,
inference(orient,[status(thm)],[t56865]) ).
cnf(t11477,plain,
true = ifeq(true,true,cong(sk22,sk21,sk21,sk22),true),
inference(cp,[status(thm)],[t268,t11474]) ).
cnf(t56869,plain,
true = cong(sk22,sk21,sk21,sk22),
inference(step,[status(thm)],[t11477,t256]) ).
cnf(t11542,plain,
cong(sk22,sk21,sk21,sk22) = true,
inference(orient,[status(thm)],[t56869]) ).
cnf(t11544,plain,
true = ifeq(true,true,cong(sk21,sk22,sk22,sk21),true),
inference(cp,[status(thm)],[t266,t11542]) ).
cnf(t56870,plain,
true = cong(sk21,sk22,sk22,sk21),
inference(step,[status(thm)],[t11544,t256]) ).
cnf(t11552,plain,
cong(sk21,sk22,sk22,sk21) = true,
inference(orient,[status(thm)],[t56870]) ).
cnf(t11554,plain,
true = ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t268,t11552]) ).
cnf(t56871,plain,
true = cong(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t11554,t256]) ).
cnf(t11561,plain,
cong(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t56871]) ).
cnf(t11571,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk22,sk22),true,midp(sk21,sk22,sk22),true),true),
inference(cp,[status(thm)],[t272,t11561]) ).
cnf(t56872,plain,
true = ifeq(coll(sk21,sk22,sk22),true,midp(sk21,sk22,sk22),true),
inference(step,[status(thm)],[t11571,t256]) ).
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(t116,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)],[t116]) ).
cnf(hi18,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X2,X3,X0,X1,X6,X7,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h545,plain,
eqangle(V0,V1,sk22,sk20,V0,V1,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi18,h128]) ).
cnf(hi21,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(eqangle(X4,X5,X6,X7,X8,X9,X10,X11),true,eqangle(X0,X1,X2,X3,X8,X9,X10,X11),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t52,plain,
eqangle(sk21,sk22,sk22,sk20,sk21,sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi21,h239,h545]) ).
cnf(t1846,plain,
eqangle(sk21,sk22,sk22,sk20,sk21,sk22,sk22,sk20) = true,
inference(orient,[status(thm)],[t52]) ).
cnf(t1849,plain,
true = ifeq(true,true,para(sk21,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t314,t1846]) ).
cnf(t56473,plain,
true = para(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t1849,t256]) ).
cnf(t3980,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t56473]) ).
cnf(t3981,plain,
true = ifeq(true,true,coll(sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t353,t3980]) ).
cnf(t56474,plain,
true = coll(sk21,sk22,sk22),
inference(step,[status(thm)],[t3981,t256]) ).
cnf(t4007,plain,
coll(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t56474]) ).
cnf(t56873,plain,
true = ifeq(true,true,midp(sk21,sk22,sk22),true),
inference(step,[status(thm)],[t56872,t4007]) ).
cnf(t56874,plain,
true = midp(sk21,sk22,sk22),
inference(step,[status(thm)],[t56873,t256]) ).
cnf(t11600,plain,
midp(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t56874]) ).
cnf(t54681,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t54680,t11600]) ).
cnf(t60520,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t54681,t256]) ).
cnf(t54689,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t60520]) ).
cnf(t54690,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t336,t54689]) ).
cnf(t60524,plain,
true = cong(sk21,X1,sk21,X1),
inference(step,[status(thm)],[t54690,t256]) ).
cnf(t54769,plain,
cong(sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t60524]) ).
cnf(t54784,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t54769]) ).
cnf(t60529,plain,
true = ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t54784,t256]) ).
cnf(t60530,plain,
true = ifeq(true,true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t60529,t54769]) ).
cnf(t60531,plain,
true = perp(sk21,sk21,X2,X1),
inference(step,[status(thm)],[t60530,t256]) ).
cnf(t54985,plain,
perp(sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t60531]) ).
cnf(t54986,plain,
true = ifeq(true,true,perp(X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t292,t54985]) ).
cnf(t60545,plain,
true = perp(X1,X2,sk21,sk21),
inference(step,[status(thm)],[t54986,t256]) ).
cnf(t55244,plain,
perp(X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t60545]) ).
cnf(t55251,plain,
true = ifeq(true,true,ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t55244]) ).
cnf(t60553,plain,
true = ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t55251,t256]) ).
cnf(t60554,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t60553,t54985]) ).
cnf(t60555,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t60554,t256]) ).
cnf(t55481,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t60555]) ).
cnf(t60556,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t346,t55481]) ).
cnf(t60557,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t60556,t256]) ).
cnf(t55482,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t60557]) ).
cnf(t56073,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t55482]) ).
cnf(t56075,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t312,t56073]) ).
cnf(t60629,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t56075,t256]) ).
cnf(t56178,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t60629]) ).
cnf(t56180,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t306,t56178]) ).
cnf(t60648,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t56180,t256]) ).
cnf(t56325,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t60648]) ).
cnf(t56332,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,t56325]) ).
cnf(t60663,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t56332,t56178]) ).
cnf(t60664,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t60663,t256]) ).
cnf(t60665,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t60664,t256]) ).
cnf(t56440,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t60665]) ).
cnf(c118,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)],[c118]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t56440]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO581+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 12:23:14 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 201.79/26.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 201.79/26.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------