%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO590+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 : n011.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 01:18:14 PM UTC 2026
% Result : Theorem 256.99s 33.34s
% Output : Proof 256.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 22
% Syntax : Number of formulae : 264 ( 180 unt; 0 def)
% Number of atoms : 408 ( 176 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 240 ( 96 ~; 90 |; 32 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 730 ( 83 sgn 276 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,conjecture,
! [C,D,E,O,A,F] :
( ( coll(F,D,E)
& coll(F,C,A)
& perp(E,O,E,A)
& perp(C,D,C,A)
& midp(O,D,C)
& perp(E,C,E,D) )
=> cong(A,E,A,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL416052) ).
fof(f94_neg,negated_conjecture,
~ ! [C,D,E,O,A,F] :
( ( coll(F,D,E)
& coll(F,C,A)
& perp(E,O,E,A)
& perp(C,D,C,A)
& midp(O,D,C)
& perp(E,C,E,D) )
=> cong(A,E,A,F) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [C,D,E,O,A,F] :
( ~ cong(A,E,A,F)
& coll(F,D,E)
& coll(F,C,A)
& perp(E,O,E,A)
& perp(C,D,C,A)
& midp(O,D,C)
& perp(E,C,E,D) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cong(sk24,sk22,sk24,sk25)
& coll(sk25,sk21,sk22)
& coll(sk25,sk20,sk24)
& perp(sk22,sk23,sk22,sk24)
& perp(sk20,sk21,sk20,sk24)
& midp(sk23,sk21,sk20)
& perp(sk22,sk20,sk22,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25])],[f94_nnf]) ).
cnf(c119,plain,
~ cong(sk24,sk22,sk24,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t27,plain,
cong(sk24,sk22,sk24,sk25) = false,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(t3493,plain,
cong(sk24,sk22,sk24,sk25) = false,
inference(orient,[status(thm)],[t27]) ).
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(t127,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t351,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t127]) ).
cnf(t3495,plain,
true = ifeq(midp(sk24,sk22,sk25),true,false,true),
inference(cp,[status(thm)],[t351,t3493]) ).
cnf(t6253,plain,
ifeq(midp(sk24,sk22,sk25),true,false,true) = true,
inference(orient,[status(thm)],[t3495]) ).
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(t215,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(t341,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)],[t215]) ).
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(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(t265,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/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(t141,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t274,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t141]) ).
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(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(t289,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(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/sandbox2/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(t152,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)],[t152]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
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(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(h67,plain,
para(sk22,sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi113,h4]) ).
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(h414,plain,
eqangle(sk22,sk20,V0,V1,sk22,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h67]) ).
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/sandbox2/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(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(t57,plain,
eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi18,h414]) ).
cnf(t1758,plain,
eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20) = true,
inference(orient,[status(thm)],[t57]) ).
cnf(t1762,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t1758]) ).
cnf(t37,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t37]) ).
cnf(t48293,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t1762,t256]) ).
cnf(t4506,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t48293]) ).
cnf(t4525,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)],[t341,t4506]) ).
cnf(t50702,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)],[t4525,t256]) ).
cnf(t50703,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t50702,t4506]) ).
cnf(t50704,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t50703,t256]) ).
cnf(t32342,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t50704]) ).
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(t158,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(t290,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)],[t158]) ).
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(t157,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)],[t157]) ).
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(t119,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)],[t119]) ).
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(t120,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)],[t120]) ).
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(t128,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t337,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t128]) ).
cnf(t4507,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t337,t4506]) ).
cnf(t48294,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t4507,t256]) ).
cnf(t4535,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t48294]) ).
cnf(t4537,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t4535]) ).
cnf(t48295,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t4537,t256]) ).
cnf(t4579,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t48295]) ).
cnf(t4582,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t4579]) ).
cnf(t48296,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t4582,t256]) ).
cnf(t4611,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t48296]) ).
cnf(t4614,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t4611]) ).
cnf(t48297,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t4614,t256]) ).
cnf(t48298,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t48297,t4611]) ).
cnf(t48299,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t48298,t256]) ).
cnf(t4646,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t48299]) ).
cnf(t48310,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t290,t4646]) ).
cnf(t48311,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t48310,t256]) ).
cnf(t4653,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t48311]) ).
cnf(t33983,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t4653]) ).
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/sandbox2/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(t246,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)],[t246]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox2/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(t151,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)],[t151]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD14) ).
fof(f13_nnf,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t135,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t364,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t135]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/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(t136,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)],[t136]) ).
cnf(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h413,plain,
coll(sk22,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi66,h67]) ).
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(h1458,plain,
coll(sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h413,h413]) ).
cnf(h7642,plain,
coll(sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1458,h1458]) ).
cnf(h68,plain,
para(sk22,sk21,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h4,hi113]) ).
cnf(h417,plain,
eqangle(sk22,sk21,V0,V1,sk22,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h68]) ).
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/sandbox2/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(t32,plain,
cyclic(sk21,sk20,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h417,h7642]) ).
cnf(t3023,plain,
cyclic(sk21,sk20,sk22,sk22) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t3024,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk20,sk22),true),
inference(cp,[status(thm)],[t362,t3023]) ).
cnf(t48381,plain,
true = cyclic(sk21,sk22,sk20,sk22),
inference(step,[status(thm)],[t3024,t256]) ).
cnf(t4864,plain,
cyclic(sk21,sk22,sk20,sk22) = true,
inference(orient,[status(thm)],[t48381]) ).
cnf(t4865,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk22,sk20),true),
inference(cp,[status(thm)],[t364,t4864]) ).
cnf(t48410,plain,
true = cyclic(sk21,sk22,sk22,sk20),
inference(step,[status(thm)],[t4865,t256]) ).
cnf(t5369,plain,
cyclic(sk21,sk22,sk22,sk20) = true,
inference(orient,[status(thm)],[t48410]) ).
cnf(t5372,plain,
true = ifeq(true,true,eqangle(sk22,sk21,sk22,sk22,sk20,sk21,sk20,sk22),true),
inference(cp,[status(thm)],[t359,t5369]) ).
cnf(t48628,plain,
true = eqangle(sk22,sk21,sk22,sk22,sk20,sk21,sk20,sk22),
inference(step,[status(thm)],[t5372,t256]) ).
cnf(t8002,plain,
eqangle(sk22,sk21,sk22,sk22,sk20,sk21,sk20,sk22) = true,
inference(orient,[status(thm)],[t48628]) ).
cnf(t8015,plain,
true = ifeq(cyclic(sk21,sk22,sk22,sk21),true,ifeq(cyclic(sk21,sk22,sk22,sk22),true,ifeq(cyclic(sk21,sk22,sk22,sk20),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),true),
inference(cp,[status(thm)],[t357,t8002]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c118,plain,
coll(sk25,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
coll(sk25,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h31,plain,
coll(sk21,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi118]) ).
cnf(h136,plain,
coll(sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h31,h31]) ).
cnf(t33,plain,
cyclic(sk21,sk21,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h417,h136]) ).
cnf(t3054,plain,
cyclic(sk21,sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t3055,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t362,t3054]) ).
cnf(t48383,plain,
true = cyclic(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t3055,t256]) ).
cnf(t4894,plain,
cyclic(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t48383]) ).
cnf(t4895,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk22,sk21),true),
inference(cp,[status(thm)],[t364,t4894]) ).
cnf(t48413,plain,
true = cyclic(sk21,sk22,sk22,sk21),
inference(step,[status(thm)],[t4895,t256]) ).
cnf(t5412,plain,
cyclic(sk21,sk22,sk22,sk21) = true,
inference(orient,[status(thm)],[t48413]) ).
cnf(t48629,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk22,sk22,sk22),true,ifeq(cyclic(sk21,sk22,sk22,sk20),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),true),
inference(step,[status(thm)],[t8015,t5412]) ).
cnf(t48630,plain,
true = ifeq(cyclic(sk21,sk22,sk22,sk22),true,ifeq(cyclic(sk21,sk22,sk22,sk20),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),
inference(step,[status(thm)],[t48629,t256]) ).
cnf(h30,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi118,hi118]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h123,plain,
coll(sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h30]) ).
cnf(h374,plain,
coll(sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h123,h123]) ).
cnf(t34,plain,
cyclic(sk21,sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h417,h374]) ).
cnf(t3039,plain,
cyclic(sk21,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t48631,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk22,sk22,sk20),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),
inference(step,[status(thm)],[t48630,t3039]) ).
cnf(t48632,plain,
true = ifeq(cyclic(sk21,sk22,sk22,sk20),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),
inference(step,[status(thm)],[t48631,t256]) ).
cnf(t48633,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),
inference(step,[status(thm)],[t48632,t5369]) ).
cnf(t48634,plain,
true = ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),
inference(step,[status(thm)],[t48633,t256]) ).
cnf(t48635,plain,
true = cong(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t48634,t256]) ).
cnf(t8016,plain,
cong(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t48635]) ).
cnf(t34001,plain,
true = ifeq(true,true,midp(sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t33983,t8016]) ).
cnf(t50842,plain,
true = midp(sk21,sk22,sk22),
inference(step,[status(thm)],[t34001,t256]) ).
cnf(t34216,plain,
midp(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t50842]) ).
cnf(t34217,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t32342,t34216]) ).
cnf(t50849,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t34217,t256]) ).
cnf(t34373,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t50849]) ).
cnf(t34382,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t351,t34373]) ).
cnf(t50904,plain,
true = cong(sk21,X1,sk21,X1),
inference(step,[status(thm)],[t34382,t256]) ).
cnf(t35310,plain,
cong(sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t50904]) ).
cnf(t35321,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),true),
inference(cp,[status(thm)],[t289,t35310]) ).
cnf(t50988,plain,
true = ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t35321,t256]) ).
cnf(t50989,plain,
true = ifeq(true,true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t50988,t35310]) ).
cnf(t50990,plain,
true = perp(sk21,sk21,X2,X1),
inference(step,[status(thm)],[t50989,t256]) ).
cnf(t36905,plain,
perp(sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t50990]) ).
cnf(t36912,plain,
true = ifeq(true,true,perp(X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t274,t36905]) ).
cnf(t51095,plain,
true = perp(X1,X2,sk21,sk21),
inference(step,[status(thm)],[t36912,t256]) ).
cnf(t38644,plain,
perp(X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t51095]) ).
cnf(t38662,plain,
true = ifeq(true,true,ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t38644]) ).
cnf(t51195,plain,
true = ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t38662,t256]) ).
cnf(t51196,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t51195,t36905]) ).
cnf(t51197,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t51196,t256]) ).
cnf(t40455,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t51197]) ).
cnf(t51233,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)],[t341,t40455]) ).
cnf(t51234,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)],[t51233,t256]) ).
cnf(t51235,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t51234,t40455]) ).
cnf(t51236,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t51235,t256]) ).
cnf(t40478,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t51236]) ).
cnf(t48151,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t40478]) ).
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(t133,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t286,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t133]) ).
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(t134,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t284,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t134]) ).
cnf(t35313,plain,
true = ifeq(true,true,cong(sk21,X1,X1,sk21),true),
inference(cp,[status(thm)],[t286,t35310]) ).
cnf(t50987,plain,
true = cong(sk21,X1,X1,sk21),
inference(step,[status(thm)],[t35313,t256]) ).
cnf(t36877,plain,
cong(sk21,X1,X1,sk21) = true,
inference(orient,[status(thm)],[t50987]) ).
cnf(t36879,plain,
true = ifeq(true,true,cong(X1,sk21,sk21,X1),true),
inference(cp,[status(thm)],[t284,t36877]) ).
cnf(t51091,plain,
true = cong(X1,sk21,sk21,X1),
inference(step,[status(thm)],[t36879,t256]) ).
cnf(t38575,plain,
cong(X1,sk21,sk21,X1) = true,
inference(orient,[status(thm)],[t51091]) ).
cnf(t38577,plain,
true = ifeq(true,true,cong(X1,sk21,X1,sk21),true),
inference(cp,[status(thm)],[t286,t38575]) ).
cnf(t51173,plain,
true = cong(X1,sk21,X1,sk21),
inference(step,[status(thm)],[t38577,t256]) ).
cnf(t40179,plain,
cong(X1,sk21,X1,sk21) = true,
inference(orient,[status(thm)],[t51173]) ).
cnf(t40180,plain,
true = ifeq(true,true,midp(X1,sk21,sk21),true),
inference(cp,[status(thm)],[t33983,t40179]) ).
cnf(t51174,plain,
true = midp(X1,sk21,sk21),
inference(step,[status(thm)],[t40180,t256]) ).
cnf(t40207,plain,
midp(X1,sk21,sk21) = true,
inference(orient,[status(thm)],[t51174]) ).
cnf(t40210,plain,
true = ifeq(true,true,midp(X1,X2,X2),true),
inference(cp,[status(thm)],[t32342,t40207]) ).
cnf(t51175,plain,
true = midp(X1,X2,X2),
inference(step,[status(thm)],[t40210,t256]) ).
cnf(t40230,plain,
midp(X1,X2,X2) = true,
inference(orient,[status(thm)],[t51175]) ).
cnf(t48152,plain,
true = ifeq(true,true,midp(X1,X2,X3),true),
inference(cp,[status(thm)],[t48151,t40230]) ).
cnf(t51837,plain,
true = midp(X1,X2,X3),
inference(step,[status(thm)],[t48152,t256]) ).
cnf(t48232,plain,
midp(X1,X2,X3) = true,
inference(orient,[status(thm)],[t51837]) ).
cnf(t51840,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t6253,t48232]) ).
cnf(t51841,plain,
false = true,
inference(step,[status(thm)],[t51840,t256]) ).
cnf(t48234,plain,
false = true,
inference(rw,[status(thm)],[t51841]) ).
cnf(t48242,plain,
false = true,
inference(orient,[status(thm)],[t48234]) ).
cnf(t51858,plain,
cong(sk24,sk22,sk24,sk25) = true,
inference(step,[status(thm)],[t3493,t48242]) ).
cnf(t48243,plain,
cong(sk24,sk22,sk24,sk25) = true,
inference(orient,[status(thm)],[t51858]) ).
cnf(goal_0,negated_conjecture,
cong(sk24,sk22,sk24,sk25) != true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t48243]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO590+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 12:29:26 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 256.99/33.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 256.99/33.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------