%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO588+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 : n012.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 01:18:13 PM UTC 2026
% Result : Theorem 26.54s 23.40s
% Output : Proof 26.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 20
% Syntax : Number of formulae : 205 ( 129 unt; 0 def)
% Number of atoms : 361 ( 124 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 252 ( 96 ~; 90 |; 46 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-4 aty)
% Number of variables : 608 ( 32 sgn 266 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/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(t190,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)],[t190]) ).
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(t118,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)],[t118]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/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(t177,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)],[t177]) ).
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(t107,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)],[t107]) ).
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(t227,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)],[t227]) ).
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(t161,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)],[t161]) ).
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(t182,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t308,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(orient,[status(thm)],[t182]) ).
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(t162,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t330,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t162]) ).
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(t160,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)],[t160]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
fof(f94,conjecture,
! [A,C,M,B,O,D,P,R,J,NWPNT1] :
( ( coll(J,P,R)
& coll(J,M,O)
& midp(R,D,C)
& midp(P,B,A)
& coll(D,B,M)
& circle(O,B,D,NWPNT1)
& circle(O,A,C,B)
& perp(A,C,M,B)
& coll(M,A,C) )
=> para(P,O,M,R) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416050) ).
fof(f94_neg,negated_conjecture,
~ ! [A,C,M,B,O,D,P,R,J,NWPNT1] :
( ( coll(J,P,R)
& coll(J,M,O)
& midp(R,D,C)
& midp(P,B,A)
& coll(D,B,M)
& circle(O,B,D,NWPNT1)
& circle(O,A,C,B)
& perp(A,C,M,B)
& coll(M,A,C) )
=> para(P,O,M,R) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,C,M,B,O,D,P,R,J,NWPNT1] :
( ~ para(P,O,M,R)
& coll(J,P,R)
& coll(J,M,O)
& midp(R,D,C)
& midp(P,B,A)
& coll(D,B,M)
& circle(O,B,D,NWPNT1)
& circle(O,A,C,B)
& perp(A,C,M,B)
& coll(M,A,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk26,sk24,sk22,sk27)
& coll(sk28,sk26,sk27)
& coll(sk28,sk22,sk24)
& midp(sk27,sk25,sk21)
& midp(sk26,sk23,sk20)
& coll(sk25,sk23,sk22)
& circle(sk24,sk23,sk25,sk29)
& circle(sk24,sk20,sk21,sk23)
& perp(sk20,sk21,sk22,sk23)
& coll(sk22,sk20,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29])],[f94_nnf]) ).
cnf(c117,plain,
coll(sk25,sk23,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk25,sk23,sk22) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h8,plain,
coll(sk23,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi117]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h59,plain,
coll(sk22,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h8,h8]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(c114,plain,
perp(sk20,sk21,sk22,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
perp(sk20,sk21,sk22,sk23) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h3,plain,
perp(sk22,sk23,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi114]) ).
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(h49,plain,
para(sk22,sk23,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi8,h3,hi114]) ).
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(h424,plain,
eqangle(sk22,sk23,V0,V1,sk22,sk23,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h49]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(t28,plain,
cyclic(sk23,sk23,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h424,h59]) ).
cnf(t2842,plain,
cyclic(sk23,sk23,sk22,sk22) = true,
inference(orient,[status(thm)],[t28]) ).
cnf(t2845,plain,
true = ifeq(true,true,eqangle(sk22,sk23,sk22,sk23,sk22,sk23,sk22,sk23),true),
inference(cp,[status(thm)],[t359,t2842]) ).
cnf(t33,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t33]) ).
cnf(t29718,plain,
true = eqangle(sk22,sk23,sk22,sk23,sk22,sk23,sk22,sk23),
inference(step,[status(thm)],[t2845,t256]) ).
cnf(t6853,plain,
eqangle(sk22,sk23,sk22,sk23,sk22,sk23,sk22,sk23) = true,
inference(orient,[status(thm)],[t29718]) ).
cnf(t6854,plain,
true = ifeq(true,true,para(sk22,sk23,sk22,sk23),true),
inference(cp,[status(thm)],[t314,t6853]) ).
cnf(t29719,plain,
true = para(sk22,sk23,sk22,sk23),
inference(step,[status(thm)],[t6854,t256]) ).
cnf(t6868,plain,
para(sk22,sk23,sk22,sk23) = true,
inference(orient,[status(thm)],[t29719]) ).
cnf(t6872,plain,
true = ifeq(true,true,eqangle(sk22,sk23,X1,X2,sk22,sk23,X1,X2),true),
inference(cp,[status(thm)],[t330,t6868]) ).
cnf(t30113,plain,
true = eqangle(sk22,sk23,X1,X2,sk22,sk23,X1,X2),
inference(step,[status(thm)],[t6872,t256]) ).
cnf(t12762,plain,
eqangle(sk22,sk23,X1,X2,sk22,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t30113]) ).
cnf(t12767,plain,
true = ifeq(true,true,eqangle(X1,X2,sk22,sk23,X1,X2,sk22,sk23),true),
inference(cp,[status(thm)],[t308,t12762]) ).
cnf(t30540,plain,
true = eqangle(X1,X2,sk22,sk23,X1,X2,sk22,sk23),
inference(step,[status(thm)],[t12767,t256]) ).
cnf(t16901,plain,
eqangle(X1,X2,sk22,sk23,X1,X2,sk22,sk23) = true,
inference(orient,[status(thm)],[t30540]) ).
cnf(t16903,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t16901]) ).
cnf(t30541,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t16903,t256]) ).
cnf(t16925,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t30541]) ).
cnf(t16941,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,t16925]) ).
cnf(t31824,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)],[t16941,t256]) ).
cnf(t31825,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t31824,t16925]) ).
cnf(t31826,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t31825,t256]) ).
cnf(t28741,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t31826]) ).
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(t168,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)],[t168]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t253,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t357,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
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(t113,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)],[t113]) ).
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(t114,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t360,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t114]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(c119,plain,
midp(sk27,sk25,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
midp(sk27,sk25,sk21) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h32,plain,
cong(sk27,sk25,sk27,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi119]) ).
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(t32,plain,
cyclic(sk25,sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi12,h32,h32,h32]) ).
cnf(t3040,plain,
cyclic(sk25,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t3041,plain,
true = ifeq(true,true,cyclic(sk21,sk25,sk21,sk21),true),
inference(cp,[status(thm)],[t360,t3040]) ).
cnf(t29623,plain,
true = cyclic(sk21,sk25,sk21,sk21),
inference(step,[status(thm)],[t3041,t256]) ).
cnf(t5176,plain,
cyclic(sk21,sk25,sk21,sk21) = true,
inference(orient,[status(thm)],[t29623]) ).
cnf(t5177,plain,
true = ifeq(true,true,cyclic(sk21,sk21,sk25,sk21),true),
inference(cp,[status(thm)],[t362,t5176]) ).
cnf(t29656,plain,
true = cyclic(sk21,sk21,sk25,sk21),
inference(step,[status(thm)],[t5177,t256]) ).
cnf(t5793,plain,
cyclic(sk21,sk21,sk25,sk21) = true,
inference(orient,[status(thm)],[t29656]) ).
cnf(t5796,plain,
true = ifeq(true,true,eqangle(sk25,sk21,sk25,sk21,sk21,sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t359,t5793]) ).
cnf(t29990,plain,
true = eqangle(sk25,sk21,sk25,sk21,sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t5796,t256]) ).
cnf(t11719,plain,
eqangle(sk25,sk21,sk25,sk21,sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t29990]) ).
cnf(t11732,plain,
true = ifeq(cyclic(sk21,sk21,sk25,sk21),true,ifeq(cyclic(sk21,sk21,sk25,sk21),true,ifeq(cyclic(sk21,sk21,sk25,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),true),
inference(cp,[status(thm)],[t357,t11719]) ).
cnf(t29991,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk21,sk25,sk21),true,ifeq(cyclic(sk21,sk21,sk25,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),true),
inference(step,[status(thm)],[t11732,t5793]) ).
cnf(t29992,plain,
true = ifeq(cyclic(sk21,sk21,sk25,sk21),true,ifeq(cyclic(sk21,sk21,sk25,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),
inference(step,[status(thm)],[t29991,t256]) ).
cnf(t29993,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk21,sk25,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),
inference(step,[status(thm)],[t29992,t5793]) ).
cnf(t29994,plain,
true = ifeq(cyclic(sk21,sk21,sk25,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),
inference(step,[status(thm)],[t29993,t256]) ).
cnf(t29995,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),
inference(step,[status(thm)],[t29994,t5793]) ).
cnf(t29996,plain,
true = ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),
inference(step,[status(thm)],[t29995,t256]) ).
cnf(t29997,plain,
true = cong(sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t29996,t256]) ).
cnf(t11734,plain,
cong(sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t29997]) ).
cnf(t11743,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk21,sk21),true,midp(sk21,sk21,sk21),true),true),
inference(cp,[status(thm)],[t290,t11734]) ).
cnf(t29998,plain,
true = ifeq(coll(sk21,sk21,sk21),true,midp(sk21,sk21,sk21),true),
inference(step,[status(thm)],[t11743,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(t108,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)],[t108]) ).
cnf(t5179,plain,
true = ifeq(true,true,eqangle(sk21,sk21,sk21,sk25,sk21,sk21,sk21,sk25),true),
inference(cp,[status(thm)],[t359,t5176]) ).
cnf(t29919,plain,
true = eqangle(sk21,sk21,sk21,sk25,sk21,sk21,sk21,sk25),
inference(step,[status(thm)],[t5179,t256]) ).
cnf(t11040,plain,
eqangle(sk21,sk21,sk21,sk25,sk21,sk21,sk21,sk25) = true,
inference(orient,[status(thm)],[t29919]) ).
cnf(t11042,plain,
true = ifeq(true,true,para(sk21,sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t314,t11040]) ).
cnf(t29920,plain,
true = para(sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t11042,t256]) ).
cnf(t11054,plain,
para(sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t29920]) ).
cnf(t11055,plain,
true = ifeq(true,true,coll(sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t337,t11054]) ).
cnf(t29921,plain,
true = coll(sk21,sk21,sk21),
inference(step,[status(thm)],[t11055,t256]) ).
cnf(t11074,plain,
coll(sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t29921]) ).
cnf(t29999,plain,
true = ifeq(true,true,midp(sk21,sk21,sk21),true),
inference(step,[status(thm)],[t29998,t11074]) ).
cnf(t30000,plain,
true = midp(sk21,sk21,sk21),
inference(step,[status(thm)],[t29999,t256]) ).
cnf(t11772,plain,
midp(sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t30000]) ).
cnf(t28742,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t28741,t11772]) ).
cnf(t31827,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t28742,t256]) ).
cnf(t28752,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t31827]) ).
cnf(t28753,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t351,t28752]) ).
cnf(t31831,plain,
true = cong(sk21,X1,sk21,X1),
inference(step,[status(thm)],[t28753,t256]) ).
cnf(t28832,plain,
cong(sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t31831]) ).
cnf(t28843,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),true),
inference(cp,[status(thm)],[t289,t28832]) ).
cnf(t31836,plain,
true = ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t28843,t256]) ).
cnf(t31837,plain,
true = ifeq(true,true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t31836,t28832]) ).
cnf(t31838,plain,
true = perp(sk21,sk21,X2,X1),
inference(step,[status(thm)],[t31837,t256]) ).
cnf(t28980,plain,
perp(sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t31838]) ).
cnf(t28983,plain,
true = ifeq(true,true,perp(X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t274,t28980]) ).
cnf(t31854,plain,
true = perp(X1,X2,sk21,sk21),
inference(step,[status(thm)],[t28983,t256]) ).
cnf(t29220,plain,
perp(X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t31854]) ).
cnf(t29234,plain,
true = ifeq(true,true,ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t29220]) ).
cnf(t31869,plain,
true = ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t29234,t256]) ).
cnf(t31870,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t31869,t28980]) ).
cnf(t31871,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t31870,t256]) ).
cnf(t29538,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t31871]) ).
cnf(c122,plain,
~ para(sk26,sk24,sk22,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk26,sk24,sk22,sk27) != true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t29538]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO588+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 12:28:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.54/23.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.54/23.40 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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