%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO542+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 : n006.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 01:18:07 PM UTC 2026
% Result : Theorem 132.90s 24.12s
% Output : Proof 132.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 99
% Number of leaves : 25
% Syntax : Number of formulae : 294 ( 198 unt; 0 def)
% Number of atoms : 454 ( 194 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 274 ( 114 ~; 108 |; 27 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 941 ( 154 sgn 344 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(t167,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)],[t167]) ).
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(t75,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)],[t75]) ).
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(t76,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)],[t76]) ).
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(t73,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t316,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t73]) ).
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(t222,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(t313,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)],[t222]) ).
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(t180,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(t322,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)],[t180]) ).
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(t83,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t327,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t83]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t200,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t285,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t200]) ).
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(t173,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(t286,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)],[t173]) ).
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(t170,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(t292,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)],[t170]) ).
fof(f44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD44) ).
fof(f44_nnf,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [E,A,B,F,C] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( para(X3,X4,X1,X2)
| ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi44,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X3,X1,X4),true,para(X0,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
fof(f94,conjecture,
! [A,B,C,A1,B1,C1,O] :
( ( circle(O,A,B,C)
& midp(C1,B,A)
& midp(B1,C,A)
& midp(A1,C,B) )
=> perp(O,A1,B1,C1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012002) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,A1,B1,C1,O] :
( ( circle(O,A,B,C)
& midp(C1,B,A)
& midp(B1,C,A)
& midp(A1,C,B) )
=> perp(O,A1,B1,C1) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,A1,B1,C1,O] :
( ~ perp(O,A1,B1,C1)
& circle(O,A,B,C)
& midp(C1,B,A)
& midp(B1,C,A)
& midp(A1,C,B) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk26,sk23,sk24,sk25)
& circle(sk26,sk20,sk21,sk22)
& midp(sk25,sk21,sk20)
& midp(sk24,sk22,sk20)
& midp(sk23,sk22,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26])],[f94_nnf]) ).
cnf(c113,plain,
midp(sk23,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
midp(sk23,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(c114,plain,
midp(sk24,sk22,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
midp(sk24,sk22,sk20) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h25,plain,
para(sk23,sk24,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi44,hi113,hi114]) ).
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(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(t34,plain,
eqangle(sk23,sk24,X1,X2,sk21,sk20,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h25]) ).
cnf(t1732,plain,
eqangle(sk23,sk24,X1,X2,sk21,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t1735,plain,
true = ifeq(true,true,eqangle(sk23,sk24,sk21,sk20,X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t292,t1732]) ).
cnf(t30,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t30]) ).
cnf(t20079,plain,
true = eqangle(sk23,sk24,sk21,sk20,X1,X2,X1,X2),
inference(step,[status(thm)],[t1735,t256]) ).
cnf(t7053,plain,
eqangle(sk23,sk24,sk21,sk20,X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t20079]) ).
cnf(t7058,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk23,sk24,sk21,sk20),true),
inference(cp,[status(thm)],[t286,t7053]) ).
cnf(t20241,plain,
true = eqangle(X1,X2,X1,X2,sk23,sk24,sk21,sk20),
inference(step,[status(thm)],[t7058,t256]) ).
cnf(t9466,plain,
eqangle(X1,X2,X1,X2,sk23,sk24,sk21,sk20) = true,
inference(orient,[status(thm)],[t20241]) ).
cnf(t9471,plain,
true = ifeq(true,true,ifeq(para(sk23,sk24,sk21,sk20),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t9466]) ).
cnf(t20242,plain,
true = ifeq(para(sk23,sk24,sk21,sk20),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t9471,t256]) ).
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(t147,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(t294,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t147]) ).
cnf(t1734,plain,
true = ifeq(true,true,para(sk23,sk24,sk21,sk20),true),
inference(cp,[status(thm)],[t294,t1732]) ).
cnf(t19970,plain,
true = para(sk23,sk24,sk21,sk20),
inference(step,[status(thm)],[t1734,t256]) ).
cnf(t4679,plain,
para(sk23,sk24,sk21,sk20) = true,
inference(orient,[status(thm)],[t19970]) ).
cnf(t20243,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t20242,t4679]) ).
cnf(t20244,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t20243,t256]) ).
cnf(t9476,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t20244]) ).
cnf(t9493,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)],[t313,t9476]) ).
cnf(t21040,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)],[t9493,t256]) ).
cnf(t21041,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t21040,t9476]) ).
cnf(t21042,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t21041,t256]) ).
cnf(t16838,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t21042]) ).
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(t153,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)],[t153]) ).
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(t369,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]) ).
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(t146,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(t371,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t146]) ).
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(t78,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t374,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t78]) ).
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(t79,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t372,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t79]) ).
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,sk22,sk23,sk21) = 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(h100,plain,
cong(sk23,sk21,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi23,h5]) ).
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(t27,plain,
cyclic(sk21,sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi12,h100,h100,h100]) ).
cnf(t3505,plain,
cyclic(sk21,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t3506,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t372,t3505]) ).
cnf(t19979,plain,
true = cyclic(sk22,sk21,sk22,sk22),
inference(step,[status(thm)],[t3506,t256]) ).
cnf(t4945,plain,
cyclic(sk22,sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t19979]) ).
cnf(t4946,plain,
true = ifeq(true,true,cyclic(sk22,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t374,t4945]) ).
cnf(t19999,plain,
true = cyclic(sk22,sk22,sk21,sk22),
inference(step,[status(thm)],[t4946,t256]) ).
cnf(t5430,plain,
cyclic(sk22,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t19999]) ).
cnf(t5433,plain,
true = ifeq(true,true,eqangle(sk21,sk22,sk21,sk22,sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t371,t5430]) ).
cnf(t20211,plain,
true = eqangle(sk21,sk22,sk21,sk22,sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t5433,t256]) ).
cnf(t9198,plain,
eqangle(sk21,sk22,sk21,sk22,sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t20211]) ).
cnf(t9211,plain,
true = ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),true),
inference(cp,[status(thm)],[t369,t9198]) ).
cnf(t20212,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),true),
inference(step,[status(thm)],[t9211,t5430]) ).
cnf(t20213,plain,
true = ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),
inference(step,[status(thm)],[t20212,t256]) ).
cnf(t20214,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),
inference(step,[status(thm)],[t20213,t5430]) ).
cnf(t20215,plain,
true = ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),
inference(step,[status(thm)],[t20214,t256]) ).
cnf(t20216,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),
inference(step,[status(thm)],[t20215,t5430]) ).
cnf(t20217,plain,
true = ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),
inference(step,[status(thm)],[t20216,t256]) ).
cnf(t20218,plain,
true = cong(sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t20217,t256]) ).
cnf(t9212,plain,
cong(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t20218]) ).
cnf(t9222,plain,
true = ifeq(true,true,ifeq(coll(sk22,sk22,sk22),true,midp(sk22,sk22,sk22),true),true),
inference(cp,[status(thm)],[t272,t9212]) ).
cnf(t20219,plain,
true = ifeq(coll(sk22,sk22,sk22),true,midp(sk22,sk22,sk22),true),
inference(step,[status(thm)],[t9222,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(t74,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)],[t74]) ).
cnf(t4948,plain,
true = ifeq(true,true,eqangle(sk22,sk22,sk22,sk21,sk22,sk22,sk22,sk21),true),
inference(cp,[status(thm)],[t371,t4945]) ).
cnf(t20185,plain,
true = eqangle(sk22,sk22,sk22,sk21,sk22,sk22,sk22,sk21),
inference(step,[status(thm)],[t4948,t256]) ).
cnf(t8933,plain,
eqangle(sk22,sk22,sk22,sk21,sk22,sk22,sk22,sk21) = true,
inference(orient,[status(thm)],[t20185]) ).
cnf(t8935,plain,
true = ifeq(true,true,para(sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t294,t8933]) ).
cnf(t20186,plain,
true = para(sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t8935,t256]) ).
cnf(t8947,plain,
para(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t20186]) ).
cnf(t8948,plain,
true = ifeq(true,true,coll(sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t353,t8947]) ).
cnf(t20187,plain,
true = coll(sk22,sk22,sk22),
inference(step,[status(thm)],[t8948,t256]) ).
cnf(t8967,plain,
coll(sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t20187]) ).
cnf(t20220,plain,
true = ifeq(true,true,midp(sk22,sk22,sk22),true),
inference(step,[status(thm)],[t20219,t8967]) ).
cnf(t20221,plain,
true = midp(sk22,sk22,sk22),
inference(step,[status(thm)],[t20220,t256]) ).
cnf(t9250,plain,
midp(sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t20221]) ).
cnf(t16839,plain,
true = ifeq(true,true,midp(sk22,X1,X1),true),
inference(cp,[status(thm)],[t16838,t9250]) ).
cnf(t21043,plain,
true = midp(sk22,X1,X1),
inference(step,[status(thm)],[t16839,t256]) ).
cnf(t16847,plain,
midp(sk22,X1,X1) = true,
inference(orient,[status(thm)],[t21043]) ).
cnf(t16848,plain,
true = ifeq(true,true,cong(sk22,X1,sk22,X1),true),
inference(cp,[status(thm)],[t316,t16847]) ).
cnf(t21046,plain,
true = cong(sk22,X1,sk22,X1),
inference(step,[status(thm)],[t16848,t256]) ).
cnf(t16907,plain,
cong(sk22,X1,sk22,X1) = true,
inference(orient,[status(thm)],[t21046]) ).
cnf(t16918,plain,
true = ifeq(true,true,ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t16907]) ).
cnf(t21050,plain,
true = ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t16918,t256]) ).
cnf(t21051,plain,
true = ifeq(true,true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t21050,t16907]) ).
cnf(t21052,plain,
true = perp(sk22,sk22,X2,X1),
inference(step,[status(thm)],[t21051,t256]) ).
cnf(t17025,plain,
perp(sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t21052]) ).
cnf(t17026,plain,
true = ifeq(true,true,perp(X1,X2,sk22,sk22),true),
inference(cp,[status(thm)],[t327,t17025]) ).
cnf(t21063,plain,
true = perp(X1,X2,sk22,sk22),
inference(step,[status(thm)],[t17026,t256]) ).
cnf(t17224,plain,
perp(X1,X2,sk22,sk22) = true,
inference(orient,[status(thm)],[t21063]) ).
cnf(t17228,plain,
true = ifeq(true,true,ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t322,t17224]) ).
cnf(t21069,plain,
true = ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t17228,t256]) ).
cnf(t21070,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t21069,t17025]) ).
cnf(t21071,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t21070,t256]) ).
cnf(t17374,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t21071]) ).
cnf(t21083,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(step,[status(thm)],[t313,t17374]) ).
cnf(t21084,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t21083,t256]) ).
cnf(t21085,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t21084,t17374]) ).
cnf(t21086,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t21085,t256]) ).
cnf(t17381,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t21086]) ).
cnf(t18095,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t17381]) ).
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(t152,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t260,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t152]) ).
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(t52,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t263,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t52]) ).
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(t53,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)],[t53]) ).
cnf(t9477,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t353,t9476]) ).
cnf(t20245,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t9477,t256]) ).
cnf(t9502,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t20245]) ).
cnf(t9504,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t9502]) ).
cnf(t20246,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t9504,t256]) ).
cnf(t9545,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t20246]) ).
cnf(t9548,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t9545]) ).
cnf(t20247,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t9548,t256]) ).
cnf(t9577,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t20247]) ).
cnf(t9580,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t9577]) ).
cnf(t20248,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t9580,t256]) ).
cnf(t20249,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t20248,t9577]) ).
cnf(t20250,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t20249,t256]) ).
cnf(t9611,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t20250]) ).
cnf(t20261,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t272,t9611]) ).
cnf(t20262,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t20261,t256]) ).
cnf(t9618,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t20262]) ).
cnf(t19774,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t9618]) ).
cnf(t14,plain,
midp(sk23,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t1938,plain,
midp(sk23,sk22,sk21) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t18118,plain,
true = ifeq(true,true,midp(sk23,X1,X2),true),
inference(cp,[status(thm)],[t18095,t1938]) ).
cnf(t21173,plain,
true = midp(sk23,X1,X2),
inference(step,[status(thm)],[t18118,t256]) ).
cnf(t18167,plain,
midp(sk23,X1,X2) = true,
inference(orient,[status(thm)],[t21173]) ).
cnf(t18168,plain,
true = ifeq(true,true,cong(sk23,X1,sk23,X2),true),
inference(cp,[status(thm)],[t316,t18167]) ).
cnf(t21179,plain,
true = cong(sk23,X1,sk23,X2),
inference(step,[status(thm)],[t18168,t256]) ).
cnf(t18316,plain,
cong(sk23,X1,sk23,X2) = true,
inference(orient,[status(thm)],[t21179]) ).
cnf(t18318,plain,
true = ifeq(true,true,cong(sk23,X1,X2,sk23),true),
inference(cp,[status(thm)],[t268,t18316]) ).
cnf(t21215,plain,
true = cong(sk23,X1,X2,sk23),
inference(step,[status(thm)],[t18318,t256]) ).
cnf(t18498,plain,
cong(sk23,X1,X2,sk23) = true,
inference(orient,[status(thm)],[t21215]) ).
cnf(t18500,plain,
true = ifeq(true,true,cong(X1,sk23,sk23,X2),true),
inference(cp,[status(thm)],[t266,t18498]) ).
cnf(t21229,plain,
true = cong(X1,sk23,sk23,X2),
inference(step,[status(thm)],[t18500,t256]) ).
cnf(t18648,plain,
cong(X1,sk23,sk23,X2) = true,
inference(orient,[status(thm)],[t21229]) ).
cnf(t18650,plain,
true = ifeq(true,true,cong(X1,sk23,X2,sk23),true),
inference(cp,[status(thm)],[t268,t18648]) ).
cnf(t21236,plain,
true = cong(X1,sk23,X2,sk23),
inference(step,[status(thm)],[t18650,t256]) ).
cnf(t18783,plain,
cong(X1,sk23,X2,sk23) = true,
inference(orient,[status(thm)],[t21236]) ).
cnf(t19787,plain,
true = ifeq(true,true,midp(X1,sk23,sk23),true),
inference(cp,[status(thm)],[t19774,t18783]) ).
cnf(t21343,plain,
true = midp(X1,sk23,sk23),
inference(step,[status(thm)],[t19787,t256]) ).
cnf(t19804,plain,
midp(X1,sk23,sk23) = true,
inference(orient,[status(thm)],[t21343]) ).
cnf(t19805,plain,
true = ifeq(true,true,midp(X1,X2,X3),true),
inference(cp,[status(thm)],[t18095,t19804]) ).
cnf(t21349,plain,
true = midp(X1,X2,X3),
inference(step,[status(thm)],[t19805,t256]) ).
cnf(t19852,plain,
midp(X1,X2,X3) = true,
inference(orient,[status(thm)],[t21349]) ).
cnf(t21350,plain,
ifeq(true,true,cong(X1,X2,X1,X3),true) = true,
inference(step,[status(thm)],[t316,t19852]) ).
cnf(t21351,plain,
cong(X1,X2,X1,X3) = true,
inference(step,[status(thm)],[t21350,t256]) ).
cnf(t19853,plain,
cong(X1,X2,X1,X3) = true,
inference(rw,[status(thm)],[t21351]) ).
cnf(t19859,plain,
cong(X1,X2,X1,X3) = true,
inference(orient,[status(thm)],[t19853]) ).
cnf(t19861,plain,
true = ifeq(true,true,cong(X1,X2,X3,X1),true),
inference(cp,[status(thm)],[t268,t19859]) ).
cnf(t21381,plain,
true = cong(X1,X2,X3,X1),
inference(step,[status(thm)],[t19861,t256]) ).
cnf(t19878,plain,
cong(X1,X2,X3,X1) = true,
inference(orient,[status(thm)],[t21381]) ).
cnf(t19880,plain,
true = ifeq(true,true,cong(X1,X2,X2,X3),true),
inference(cp,[status(thm)],[t266,t19878]) ).
cnf(t21387,plain,
true = cong(X1,X2,X2,X3),
inference(step,[status(thm)],[t19880,t256]) ).
cnf(t19901,plain,
cong(X1,X2,X2,X3) = true,
inference(orient,[status(thm)],[t21387]) ).
cnf(t19903,plain,
true = ifeq(true,true,cong(X1,X2,X3,X2),true),
inference(cp,[status(thm)],[t268,t19901]) ).
cnf(t21389,plain,
true = cong(X1,X2,X3,X2),
inference(step,[status(thm)],[t19903,t256]) ).
cnf(t19923,plain,
cong(X1,X2,X3,X2) = true,
inference(orient,[status(thm)],[t21389]) ).
cnf(t21390,plain,
ifeq(true,true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(step,[status(thm)],[t271,t19923]) ).
cnf(t21391,plain,
ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true) = true,
inference(step,[status(thm)],[t21390,t256]) ).
cnf(t21392,plain,
ifeq(true,true,perp(X1,X3,X2,X4),true) = true,
inference(step,[status(thm)],[t21391,t19923]) ).
cnf(t21393,plain,
perp(X1,X3,X2,X4) = true,
inference(step,[status(thm)],[t21392,t256]) ).
cnf(t19933,plain,
perp(X1,X3,X2,X4) = true,
inference(rw,[status(thm)],[t21393]) ).
cnf(t19934,plain,
perp(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t19933]) ).
cnf(c117,plain,
~ perp(sk26,sk23,sk24,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk26,sk23,sk24,sk25) != true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t19934]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO542+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/5.48 % Computer : n006.cluster.edu
% 0.19/5.48 % Model : x86_64 x86_64
% 0.19/5.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.48 % Memory : 8046.5625MB
% 0.19/5.48 % OS : Linux 6.8.0-71-generic
% 0.19/5.48 % CPULimit : 300
% 0.19/5.48 % WCLimit : 300
% 0.19/5.48 % DateTime : Wed Sep 23 12:21:02 UTC 2026
% 0.19/5.48 % CPUTime :
% 0.19/5.48 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 132.90/24.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 132.90/24.12 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------