%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO655+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 : n004.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 01:18:24 PM UTC 2026
% Result : Theorem 222.89s 28.65s
% Output : Proof 222.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 20
% Syntax : Number of formulae : 193 ( 117 unt; 0 def)
% Number of atoms : 357 ( 114 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 260 ( 96 ~; 90 |; 54 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 661 ( 32 sgn 298 !; 11 ?)
% 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(t189,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t285,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t189]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t138,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)],[t138]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t176,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t271,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t176]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(t128,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t336,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t128]) ).
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(t226,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)],[t226]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t208,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t305,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t208]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t182,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t306,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t182]) ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD21) ).
fof(f20_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t179,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t312,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t179]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD63) ).
fof(f63_nnf,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [M,A,B,C,D] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( para(X0,X2,X1,X3)
| ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi63,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X0,X3,X4),true,para(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,MIDPNT1,MIDPNT2,MIDPNT3,NWPNT4] :
( ( perp(D,F,F,G)
& circle(D,B,F,NWPNT4)
& coll(B,E,F)
& eqangle(C,B,B,E,E,B,B,A)
& coll(E,A,C)
& perp(A,C,MIDPNT3,D)
& midp(MIDPNT3,A,C)
& perp(B,C,MIDPNT2,D)
& midp(MIDPNT2,B,C)
& perp(B,A,MIDPNT1,D)
& midp(MIDPNT1,B,A) )
=> para(F,G,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULLmoreE0229) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,MIDPNT1,MIDPNT2,MIDPNT3,NWPNT4] :
( ( perp(D,F,F,G)
& circle(D,B,F,NWPNT4)
& coll(B,E,F)
& eqangle(C,B,B,E,E,B,B,A)
& coll(E,A,C)
& perp(A,C,MIDPNT3,D)
& midp(MIDPNT3,A,C)
& perp(B,C,MIDPNT2,D)
& midp(MIDPNT2,B,C)
& perp(B,A,MIDPNT1,D)
& midp(MIDPNT1,B,A) )
=> para(F,G,A,C) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,MIDPNT1,MIDPNT2,MIDPNT3,NWPNT4] :
( ~ para(F,G,A,C)
& perp(D,F,F,G)
& circle(D,B,F,NWPNT4)
& coll(B,E,F)
& eqangle(C,B,B,E,E,B,B,A)
& coll(E,A,C)
& perp(A,C,MIDPNT3,D)
& midp(MIDPNT3,A,C)
& perp(B,C,MIDPNT2,D)
& midp(MIDPNT2,B,C)
& perp(B,A,MIDPNT1,D)
& midp(MIDPNT1,B,A) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk25,sk26,sk20,sk22)
& perp(sk23,sk25,sk25,sk26)
& circle(sk23,sk21,sk25,sk30)
& coll(sk21,sk24,sk25)
& eqangle(sk22,sk21,sk21,sk24,sk24,sk21,sk21,sk20)
& coll(sk24,sk20,sk22)
& perp(sk20,sk22,sk29,sk23)
& midp(sk29,sk20,sk22)
& perp(sk21,sk22,sk28,sk23)
& midp(sk28,sk21,sk22)
& perp(sk21,sk20,sk27,sk23)
& midp(sk27,sk21,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30])],[f94_nnf]) ).
cnf(c117,plain,
midp(sk29,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
midp(sk29,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h54,plain,
para(sk20,sk20,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi63,hi117,hi117]) ).
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(t71,plain,
eqangle(sk20,sk20,X1,X2,sk22,sk22,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h54]) ).
cnf(t1974,plain,
eqangle(sk20,sk20,X1,X2,sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t71]) ).
cnf(t1977,plain,
true = ifeq(true,true,eqangle(sk20,sk20,sk22,sk22,X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t312,t1974]) ).
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(t33992,plain,
true = eqangle(sk20,sk20,sk22,sk22,X1,X2,X1,X2),
inference(step,[status(thm)],[t1977,t256]) ).
cnf(t10795,plain,
eqangle(sk20,sk20,sk22,sk22,X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t33992]) ).
cnf(t10798,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk20,sk20,sk22,sk22),true),
inference(cp,[status(thm)],[t306,t10795]) ).
cnf(t34239,plain,
true = eqangle(X1,X2,X1,X2,sk20,sk20,sk22,sk22),
inference(step,[status(thm)],[t10798,t256]) ).
cnf(t14423,plain,
eqangle(X1,X2,X1,X2,sk20,sk20,sk22,sk22) = true,
inference(orient,[status(thm)],[t34239]) ).
cnf(t14428,plain,
true = ifeq(true,true,ifeq(para(sk20,sk20,sk22,sk22),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t305,t14423]) ).
cnf(t34240,plain,
true = ifeq(para(sk20,sk20,sk22,sk22),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t14428,t256]) ).
cnf(t43,plain,
para(sk20,sk20,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi63,hi117,hi117]) ).
cnf(t2694,plain,
para(sk20,sk20,sk22,sk22) = true,
inference(orient,[status(thm)],[t43]) ).
cnf(t34241,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t34240,t2694]) ).
cnf(t34242,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t34241,t256]) ).
cnf(t14433,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t34242]) ).
cnf(t14450,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,t14433]) ).
cnf(t36201,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)],[t14450,t256]) ).
cnf(t36202,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t36201,t14433]) ).
cnf(t36203,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t36202,t256]) ).
cnf(t33081,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t36203]) ).
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(t167,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t272,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t167]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t253,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t369,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD41) ).
fof(f40_nnf,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(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(t371,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(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(t133,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t374,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t133]) ).
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(t134,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t372,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t134]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h53,plain,
cong(sk29,sk20,sk29,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi117]) ).
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(t38,plain,
cyclic(sk20,sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi12,h53,h53,h53]) ).
cnf(t3328,plain,
cyclic(sk20,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(t3329,plain,
true = ifeq(true,true,cyclic(sk22,sk20,sk22,sk22),true),
inference(cp,[status(thm)],[t372,t3328]) ).
cnf(t33700,plain,
true = cyclic(sk22,sk20,sk22,sk22),
inference(step,[status(thm)],[t3329,t256]) ).
cnf(t4913,plain,
cyclic(sk22,sk20,sk22,sk22) = true,
inference(orient,[status(thm)],[t33700]) ).
cnf(t4914,plain,
true = ifeq(true,true,cyclic(sk22,sk22,sk20,sk22),true),
inference(cp,[status(thm)],[t374,t4913]) ).
cnf(t33727,plain,
true = cyclic(sk22,sk22,sk20,sk22),
inference(step,[status(thm)],[t4914,t256]) ).
cnf(t5458,plain,
cyclic(sk22,sk22,sk20,sk22) = true,
inference(orient,[status(thm)],[t33727]) ).
cnf(t5461,plain,
true = ifeq(true,true,eqangle(sk20,sk22,sk20,sk22,sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t371,t5458]) ).
cnf(t34177,plain,
true = eqangle(sk20,sk22,sk20,sk22,sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t5461,t256]) ).
cnf(t13665,plain,
eqangle(sk20,sk22,sk20,sk22,sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t34177]) ).
cnf(t13677,plain,
true = ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),true),
inference(cp,[status(thm)],[t369,t13665]) ).
cnf(t34178,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),true),
inference(step,[status(thm)],[t13677,t5458]) ).
cnf(t34179,plain,
true = ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),
inference(step,[status(thm)],[t34178,t256]) ).
cnf(t34180,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),
inference(step,[status(thm)],[t34179,t5458]) ).
cnf(t34181,plain,
true = ifeq(cyclic(sk22,sk22,sk20,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),
inference(step,[status(thm)],[t34180,t256]) ).
cnf(t34182,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),
inference(step,[status(thm)],[t34181,t5458]) ).
cnf(t34183,plain,
true = ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),
inference(step,[status(thm)],[t34182,t256]) ).
cnf(t34184,plain,
true = cong(sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t34183,t256]) ).
cnf(t13678,plain,
cong(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t34184]) ).
cnf(t13688,plain,
true = ifeq(true,true,ifeq(coll(sk22,sk22,sk22),true,midp(sk22,sk22,sk22),true),true),
inference(cp,[status(thm)],[t272,t13678]) ).
cnf(t34185,plain,
true = ifeq(coll(sk22,sk22,sk22),true,midp(sk22,sk22,sk22),true),
inference(step,[status(thm)],[t13688,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(t129,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)],[t129]) ).
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]) ).
cnf(t4916,plain,
true = ifeq(true,true,eqangle(sk22,sk22,sk22,sk20,sk22,sk22,sk22,sk20),true),
inference(cp,[status(thm)],[t371,t4913]) ).
cnf(t34156,plain,
true = eqangle(sk22,sk22,sk22,sk20,sk22,sk22,sk22,sk20),
inference(step,[status(thm)],[t4916,t256]) ).
cnf(t13430,plain,
eqangle(sk22,sk22,sk22,sk20,sk22,sk22,sk22,sk20) = true,
inference(orient,[status(thm)],[t34156]) ).
cnf(t13432,plain,
true = ifeq(true,true,para(sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t314,t13430]) ).
cnf(t34157,plain,
true = para(sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t13432,t256]) ).
cnf(t13443,plain,
para(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t34157]) ).
cnf(t13444,plain,
true = ifeq(true,true,coll(sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t353,t13443]) ).
cnf(t34158,plain,
true = coll(sk22,sk22,sk22),
inference(step,[status(thm)],[t13444,t256]) ).
cnf(t13463,plain,
coll(sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t34158]) ).
cnf(t34186,plain,
true = ifeq(true,true,midp(sk22,sk22,sk22),true),
inference(step,[status(thm)],[t34185,t13463]) ).
cnf(t34187,plain,
true = midp(sk22,sk22,sk22),
inference(step,[status(thm)],[t34186,t256]) ).
cnf(t13716,plain,
midp(sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t34187]) ).
cnf(t33082,plain,
true = ifeq(true,true,midp(sk22,X1,X1),true),
inference(cp,[status(thm)],[t33081,t13716]) ).
cnf(t36204,plain,
true = midp(sk22,X1,X1),
inference(step,[status(thm)],[t33082,t256]) ).
cnf(t33087,plain,
midp(sk22,X1,X1) = true,
inference(orient,[status(thm)],[t36204]) ).
cnf(t33088,plain,
true = ifeq(true,true,cong(sk22,X1,sk22,X1),true),
inference(cp,[status(thm)],[t336,t33087]) ).
cnf(t36207,plain,
true = cong(sk22,X1,sk22,X1),
inference(step,[status(thm)],[t33088,t256]) ).
cnf(t33147,plain,
cong(sk22,X1,sk22,X1) = true,
inference(orient,[status(thm)],[t36207]) ).
cnf(t33163,plain,
true = ifeq(true,true,ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t33147]) ).
cnf(t36211,plain,
true = ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t33163,t256]) ).
cnf(t36212,plain,
true = ifeq(true,true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t36211,t33147]) ).
cnf(t36213,plain,
true = perp(sk22,sk22,X2,X1),
inference(step,[status(thm)],[t36212,t256]) ).
cnf(t33297,plain,
perp(sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t36213]) ).
cnf(t33298,plain,
true = ifeq(true,true,perp(X1,X2,sk22,sk22),true),
inference(cp,[status(thm)],[t292,t33297]) ).
cnf(t36223,plain,
true = perp(X1,X2,sk22,sk22),
inference(step,[status(thm)],[t33298,t256]) ).
cnf(t33474,plain,
perp(X1,X2,sk22,sk22) = true,
inference(orient,[status(thm)],[t36223]) ).
cnf(t33481,plain,
true = ifeq(true,true,ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t33474]) ).
cnf(t36229,plain,
true = ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t33481,t256]) ).
cnf(t36230,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t36229,t33297]) ).
cnf(t36231,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t36230,t256]) ).
cnf(t33640,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t36231]) ).
cnf(c124,plain,
~ para(sk25,sk26,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk25,sk26,sk20,sk22) != true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t33640]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO655+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 % Computer : n004.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Wed Sep 23 12:40:23 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 222.89/28.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 222.89/28.65 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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