%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO593+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 : n018.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 204.34s 29.32s
% Output : Proof 204.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 20
% Syntax : Number of formulae : 225 ( 149 unt; 0 def)
% Number of atoms : 381 ( 145 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 240 ( 84 ~; 78 |; 58 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 15 ( 15 usr; 14 con; 0-4 aty)
% Number of variables : 695 ( 83 sgn 264 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,conjecture,
! [B,C,A,D,O,M,G,F,E,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(E,B,M)
& coll(E,A,D)
& coll(F,B,M)
& coll(F,C,A)
& circle(O,A,G,NWPNT3)
& coll(G,B,M)
& coll(M,A,O)
& perp(M,B,A,O)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,C,B)
& coll(D,B,C)
& perp(D,A,B,C)
& perp(A,B,A,C) )
=> cong(E,A,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416055) ).
fof(f94_neg,negated_conjecture,
~ ! [B,C,A,D,O,M,G,F,E,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(E,B,M)
& coll(E,A,D)
& coll(F,B,M)
& coll(F,C,A)
& circle(O,A,G,NWPNT3)
& coll(G,B,M)
& coll(M,A,O)
& perp(M,B,A,O)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,C,B)
& coll(D,B,C)
& perp(D,A,B,C)
& perp(A,B,A,C) )
=> cong(E,A,E,F) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [B,C,A,D,O,M,G,F,E,NWPNT1,NWPNT2,NWPNT3] :
( ~ cong(E,A,E,F)
& coll(E,B,M)
& coll(E,A,D)
& coll(F,B,M)
& coll(F,C,A)
& circle(O,A,G,NWPNT3)
& coll(G,B,M)
& coll(M,A,O)
& perp(M,B,A,O)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,C,B)
& coll(D,B,C)
& perp(D,A,B,C)
& perp(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cong(sk28,sk22,sk28,sk27)
& coll(sk28,sk20,sk25)
& coll(sk28,sk22,sk23)
& coll(sk27,sk20,sk25)
& coll(sk27,sk21,sk22)
& circle(sk24,sk22,sk26,sk31)
& coll(sk26,sk20,sk25)
& coll(sk25,sk22,sk24)
& perp(sk25,sk20,sk22,sk24)
& circle(sk24,sk22,sk29,sk30)
& midp(sk24,sk21,sk20)
& coll(sk23,sk20,sk21)
& perp(sk23,sk22,sk20,sk21)
& perp(sk22,sk20,sk22,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31])],[f94_nnf]) ).
cnf(c126,plain,
~ cong(sk28,sk22,sk28,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t29,plain,
cong(sk28,sk22,sk28,sk27) = false,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(t3478,plain,
cong(sk28,sk22,sk28,sk27) = false,
inference(orient,[status(thm)],[t29]) ).
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(t104,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t335,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t104]) ).
cnf(t3480,plain,
true = ifeq(midp(sk28,sk22,sk27),true,false,true),
inference(cp,[status(thm)],[t335,t3478]) ).
cnf(t8235,plain,
ifeq(midp(sk28,sk22,sk27),true,false,true) = true,
inference(orient,[status(thm)],[t3480]) ).
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(t212,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)],[t212]) ).
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(t169,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)],[t169]) ).
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(t114,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)],[t114]) ).
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(t156,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(t266,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)],[t156]) ).
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(t141,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)],[t141]) ).
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(h60,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/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(h265,plain,
eqangle(sk22,sk20,V0,V1,sk22,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h60]) ).
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(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(t59,plain,
eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi18,h265]) ).
cnf(t1873,plain,
eqangle(X1,X2,sk22,sk20,X1,X2,sk22,sk20) = true,
inference(orient,[status(thm)],[t59]) ).
cnf(t1877,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t1873]) ).
cnf(t42,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t42]) ).
cnf(t29632,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t1877,t256]) ).
cnf(t5646,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t29632]) ).
cnf(t5666,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,t5646]) ).
cnf(t31744,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)],[t5666,t256]) ).
cnf(t31745,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t31744,t5646]) ).
cnf(t31746,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t31745,t256]) ).
cnf(t26469,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t31746]) ).
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(t147,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(t269,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)],[t147]) ).
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(t146,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(t278,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t146]) ).
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(t100,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t281,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t100]) ).
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(t101,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t279,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t101]) ).
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(t105,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)],[t105]) ).
cnf(t5647,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t353,t5646]) ).
cnf(t29633,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t5647,t256]) ).
cnf(t5675,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t29633]) ).
cnf(t5677,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t279,t5675]) ).
cnf(t29634,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t5677,t256]) ).
cnf(t5719,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t29634]) ).
cnf(t5722,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t281,t5719]) ).
cnf(t29635,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t5722,t256]) ).
cnf(t5751,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t29635]) ).
cnf(t5758,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t278,t5751]) ).
cnf(t29636,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t5758,t256]) ).
cnf(t29637,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t29636,t5751]) ).
cnf(t29638,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t29637,t256]) ).
cnf(t5786,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t29638]) ).
cnf(t29649,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t269,t5786]) ).
cnf(t29650,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t29649,t256]) ).
cnf(t5793,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t29650]) ).
cnf(t27472,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t5793]) ).
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(t106,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t263,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t106]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t157,plain,
ifeq(cong(X1,X2,X3,X4),true,ifeq(cong(X3,X4,X5,X6),true,cong(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t260,plain,
ifeq(cong(X1,X2,X3,X4),true,ifeq(cong(X3,X4,X5,X6),true,cong(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t157]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD7) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h5,plain,
perp(sk22,sk20,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi113]) ).
cnf(h64,plain,
perp(sk21,sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h5]) ).
fof(f52,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD52) ).
fof(f52_nnf,plain,
! [A,B,C,M] :
( cong(A,M,B,M)
| ~ midp(M,A,C)
| ~ perp(A,B,B,C) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [A,B,C,M] :
( cong(A,M,B,M)
| ~ midp(M,A,C)
| ~ perp(A,B,B,C) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c52,plain,
( cong(X0,X3,X1,X3)
| ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi52,axiom,
ifeq(perp(X0,X1,X1,X2),true,ifeq(midp(X3,X0,X2),true,cong(X0,X3,X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(c116,plain,
midp(sk24,sk21,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
midp(sk24,sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h313,plain,
cong(sk21,sk24,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi52,h64,hi116]) ).
cnf(hi22,axiom,
ifeq(cong(X0,X1,X2,X3),true,cong(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t26,plain,
cong(sk21,sk24,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi22,h313]) ).
cnf(t406,plain,
cong(sk21,sk24,sk24,sk22) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(t413,plain,
true = ifeq(cong(X1,X2,sk21,sk24),true,ifeq(true,true,cong(X1,X2,sk24,sk22),true),true),
inference(cp,[status(thm)],[t260,t406]) ).
cnf(t30527,plain,
true = ifeq(cong(X1,X2,sk21,sk24),true,cong(X1,X2,sk24,sk22),true),
inference(step,[status(thm)],[t413,t256]) ).
cnf(t14615,plain,
ifeq(cong(X1,X2,sk21,sk24),true,cong(X1,X2,sk24,sk22),true) = true,
inference(orient,[status(thm)],[t30527]) ).
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(hi23,axiom,
ifeq(cong(X0,X1,X2,X3),true,cong(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t27,plain,
cong(sk22,sk24,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi23,h313]) ).
cnf(t671,plain,
cong(sk22,sk24,sk21,sk24) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t14616,plain,
true = ifeq(true,true,cong(sk22,sk24,sk24,sk22),true),
inference(cp,[status(thm)],[t14615,t671]) ).
cnf(t30528,plain,
true = cong(sk22,sk24,sk24,sk22),
inference(step,[status(thm)],[t14616,t256]) ).
cnf(t14619,plain,
cong(sk22,sk24,sk24,sk22) = true,
inference(orient,[status(thm)],[t30528]) ).
cnf(t14621,plain,
true = ifeq(true,true,cong(sk22,sk24,sk22,sk24),true),
inference(cp,[status(thm)],[t263,t14619]) ).
cnf(t30530,plain,
true = cong(sk22,sk24,sk22,sk24),
inference(step,[status(thm)],[t14621,t256]) ).
cnf(t14660,plain,
cong(sk22,sk24,sk22,sk24) = true,
inference(orient,[status(thm)],[t30530]) ).
cnf(t27478,plain,
true = ifeq(true,true,midp(sk22,sk24,sk24),true),
inference(cp,[status(thm)],[t27472,t14660]) ).
cnf(t31872,plain,
true = midp(sk22,sk24,sk24),
inference(step,[status(thm)],[t27478,t256]) ).
cnf(t27543,plain,
midp(sk22,sk24,sk24) = true,
inference(orient,[status(thm)],[t31872]) ).
cnf(t27544,plain,
true = ifeq(true,true,midp(sk22,X1,X1),true),
inference(cp,[status(thm)],[t26469,t27543]) ).
cnf(t31880,plain,
true = midp(sk22,X1,X1),
inference(step,[status(thm)],[t27544,t256]) ).
cnf(t27731,plain,
midp(sk22,X1,X1) = true,
inference(orient,[status(thm)],[t31880]) ).
cnf(t27736,plain,
true = ifeq(true,true,cong(sk22,X1,sk22,X1),true),
inference(cp,[status(thm)],[t335,t27731]) ).
cnf(t31908,plain,
true = cong(sk22,X1,sk22,X1),
inference(step,[status(thm)],[t27736,t256]) ).
cnf(t28146,plain,
cong(sk22,X1,sk22,X1) = true,
inference(orient,[status(thm)],[t31908]) ).
cnf(t28164,plain,
true = ifeq(true,true,ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),true),
inference(cp,[status(thm)],[t266,t28146]) ).
cnf(t31938,plain,
true = ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t28164,t256]) ).
cnf(t31939,plain,
true = ifeq(true,true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t31938,t28146]) ).
cnf(t31940,plain,
true = perp(sk22,sk22,X2,X1),
inference(step,[status(thm)],[t31939,t256]) ).
cnf(t28645,plain,
perp(sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t31940]) ).
cnf(t28646,plain,
true = ifeq(true,true,perp(X1,X2,sk22,sk22),true),
inference(cp,[status(thm)],[t292,t28645]) ).
cnf(t31960,plain,
true = perp(X1,X2,sk22,sk22),
inference(step,[status(thm)],[t28646,t256]) ).
cnf(t28950,plain,
perp(X1,X2,sk22,sk22) = true,
inference(orient,[status(thm)],[t31960]) ).
cnf(t28957,plain,
true = ifeq(true,true,ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t28950]) ).
cnf(t31969,plain,
true = ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t28957,t256]) ).
cnf(t31970,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t31969,t28645]) ).
cnf(t31971,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t31970,t256]) ).
cnf(t29173,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t31971]) ).
cnf(t31983,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)],[t333,t29173]) ).
cnf(t31984,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)],[t31983,t256]) ).
cnf(t31985,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t31984,t29173]) ).
cnf(t31986,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t31985,t256]) ).
cnf(t29180,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t31986]) ).
cnf(t29490,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t29180]) ).
cnf(t107,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t261,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t107]) ).
cnf(t28151,plain,
true = ifeq(true,true,cong(sk22,X1,X1,sk22),true),
inference(cp,[status(thm)],[t263,t28146]) ).
cnf(t31937,plain,
true = cong(sk22,X1,X1,sk22),
inference(step,[status(thm)],[t28151,t256]) ).
cnf(t28611,plain,
cong(sk22,X1,X1,sk22) = true,
inference(orient,[status(thm)],[t31937]) ).
cnf(t28615,plain,
true = ifeq(true,true,cong(X1,sk22,sk22,X1),true),
inference(cp,[status(thm)],[t261,t28611]) ).
cnf(t31959,plain,
true = cong(X1,sk22,sk22,X1),
inference(step,[status(thm)],[t28615,t256]) ).
cnf(t28920,plain,
cong(X1,sk22,sk22,X1) = true,
inference(orient,[status(thm)],[t31959]) ).
cnf(t28924,plain,
true = ifeq(true,true,cong(X1,sk22,X1,sk22),true),
inference(cp,[status(thm)],[t263,t28920]) ).
cnf(t31966,plain,
true = cong(X1,sk22,X1,sk22),
inference(step,[status(thm)],[t28924,t256]) ).
cnf(t29095,plain,
cong(X1,sk22,X1,sk22) = true,
inference(orient,[status(thm)],[t31966]) ).
cnf(t29096,plain,
true = ifeq(true,true,midp(X1,sk22,sk22),true),
inference(cp,[status(thm)],[t27472,t29095]) ).
cnf(t31967,plain,
true = midp(X1,sk22,sk22),
inference(step,[status(thm)],[t29096,t256]) ).
cnf(t29129,plain,
midp(X1,sk22,sk22) = true,
inference(orient,[status(thm)],[t31967]) ).
cnf(t29130,plain,
true = ifeq(true,true,midp(X1,X2,X2),true),
inference(cp,[status(thm)],[t26469,t29129]) ).
cnf(t31968,plain,
true = midp(X1,X2,X2),
inference(step,[status(thm)],[t29130,t256]) ).
cnf(t29148,plain,
midp(X1,X2,X2) = true,
inference(orient,[status(thm)],[t31968]) ).
cnf(t29491,plain,
true = ifeq(true,true,midp(X1,X2,X3),true),
inference(cp,[status(thm)],[t29490,t29148]) ).
cnf(t32030,plain,
true = midp(X1,X2,X3),
inference(step,[status(thm)],[t29491,t256]) ).
cnf(t29524,plain,
midp(X1,X2,X3) = true,
inference(orient,[status(thm)],[t32030]) ).
cnf(t32045,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t8235,t29524]) ).
cnf(t32046,plain,
false = true,
inference(step,[status(thm)],[t32045,t256]) ).
cnf(t29532,plain,
false = true,
inference(rw,[status(thm)],[t32046]) ).
cnf(t29551,plain,
false = true,
inference(orient,[status(thm)],[t29532]) ).
cnf(t32062,plain,
cong(sk28,sk22,sk28,sk27) = true,
inference(step,[status(thm)],[t3478,t29551]) ).
cnf(t29552,plain,
cong(sk28,sk22,sk28,sk27) = true,
inference(orient,[status(thm)],[t32062]) ).
cnf(goal_0,negated_conjecture,
cong(sk28,sk22,sk28,sk27) != true,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t29552]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO593+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 : n018.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 12:32:02 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 204.34/29.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 204.34/29.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------