%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO611+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 : 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 01:18:17 PM UTC 2026
% Result : Theorem 61.83s 8.66s
% Output : Proof 61.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 19
% Syntax : Number of formulae : 193 ( 121 unt; 0 def)
% Number of atoms : 337 ( 116 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 234 ( 90 ~; 84 |; 41 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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 : 590 ( 32 sgn 257 !; 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/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(t193,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)],[t193]) ).
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(t180,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(t326,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)],[t180]) ).
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(t129,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t363,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t129]) ).
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(t228,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(t353,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)],[t228]) ).
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(t155,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(t311,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t155]) ).
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(t185,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(t305,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)],[t185]) ).
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(t156,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(t294,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t156]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2] :
( ( coll(H,E,G)
& circle(D,E,H,NWPNT2)
& coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) )
=> para(G,F,H,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618073) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2] :
( ( coll(H,E,G)
& circle(D,E,H,NWPNT2)
& coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) )
=> para(G,F,H,C) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2] :
( ~ para(G,F,H,C)
& coll(H,E,G)
& circle(D,E,H,NWPNT2)
& coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk26,sk25,sk27,sk22)
& coll(sk27,sk24,sk26)
& circle(sk23,sk24,sk27,sk29)
& coll(sk26,sk20,sk21)
& perp(sk26,sk24,sk20,sk21)
& coll(sk25,sk20,sk22)
& perp(sk25,sk24,sk20,sk22)
& circle(sk23,sk20,sk24,sk28)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29])],[f94_nnf]) ).
cnf(c115,plain,
perp(sk25,sk24,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
perp(sk25,sk24,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h2,plain,
perp(sk20,sk22,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi115]) ).
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(t44,plain,
para(sk25,sk24,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi115,h2]) ).
cnf(t1637,plain,
para(sk25,sk24,sk25,sk24) = true,
inference(orient,[status(thm)],[t44]) ).
cnf(t1640,plain,
true = ifeq(true,true,eqangle(sk25,sk24,X1,X2,sk25,sk24,X1,X2),true),
inference(cp,[status(thm)],[t294,t1637]) ).
cnf(t34,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t34]) ).
cnf(t19271,plain,
true = eqangle(sk25,sk24,X1,X2,sk25,sk24,X1,X2),
inference(step,[status(thm)],[t1640,t256]) ).
cnf(t5248,plain,
eqangle(sk25,sk24,X1,X2,sk25,sk24,X1,X2) = true,
inference(orient,[status(thm)],[t19271]) ).
cnf(t5255,plain,
true = ifeq(true,true,eqangle(X1,X2,sk25,sk24,X1,X2,sk25,sk24),true),
inference(cp,[status(thm)],[t305,t5248]) ).
cnf(t19570,plain,
true = eqangle(X1,X2,sk25,sk24,X1,X2,sk25,sk24),
inference(step,[status(thm)],[t5255,t256]) ).
cnf(t9466,plain,
eqangle(X1,X2,sk25,sk24,X1,X2,sk25,sk24) = true,
inference(orient,[status(thm)],[t19570]) ).
cnf(t9469,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t311,t9466]) ).
cnf(t19571,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t9469,t256]) ).
cnf(t9491,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t19571]) ).
cnf(t9507,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)],[t353,t9491]) ).
cnf(t20632,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)],[t9507,t256]) ).
cnf(t20633,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t20632,t9491]) ).
cnf(t20634,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t20633,t256]) ).
cnf(t18162,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t20634]) ).
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(t171,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(t327,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)],[t171]) ).
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(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(t341,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/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(t154,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(t343,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t154]) ).
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(t346,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t136]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox2/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(t137,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t344,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t137]) ).
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(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(c120,plain,
coll(sk27,sk24,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
coll(sk27,sk24,sk26) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h13,plain,
coll(sk26,sk26,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi120,hi120]) ).
cnf(c117,plain,
perp(sk26,sk24,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
perp(sk26,sk24,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h7,plain,
perp(sk20,sk21,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi117]) ).
cnf(h31,plain,
para(sk26,sk24,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi117,h7]) ).
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(h82,plain,
eqangle(sk26,sk24,V0,V1,sk26,sk24,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h31]) ).
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(h253,plain,
cyclic(sk24,sk27,sk26,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi42,h82,h13]) ).
fof(f16,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD17) ).
fof(f16_nnf,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,cyclic(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t33,plain,
cyclic(sk27,sk26,sk26,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi16,h253,h253]) ).
cnf(t2755,plain,
cyclic(sk27,sk26,sk26,sk26) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t2756,plain,
true = ifeq(true,true,cyclic(sk26,sk27,sk26,sk26),true),
inference(cp,[status(thm)],[t344,t2755]) ).
cnf(t19225,plain,
true = cyclic(sk26,sk27,sk26,sk26),
inference(step,[status(thm)],[t2756,t256]) ).
cnf(t4502,plain,
cyclic(sk26,sk27,sk26,sk26) = true,
inference(orient,[status(thm)],[t19225]) ).
cnf(t4503,plain,
true = ifeq(true,true,cyclic(sk26,sk26,sk27,sk26),true),
inference(cp,[status(thm)],[t346,t4502]) ).
cnf(t19245,plain,
true = cyclic(sk26,sk26,sk27,sk26),
inference(step,[status(thm)],[t4503,t256]) ).
cnf(t4857,plain,
cyclic(sk26,sk26,sk27,sk26) = true,
inference(orient,[status(thm)],[t19245]) ).
cnf(t4860,plain,
true = ifeq(true,true,eqangle(sk27,sk26,sk27,sk26,sk26,sk26,sk26,sk26),true),
inference(cp,[status(thm)],[t343,t4857]) ).
cnf(t19530,plain,
true = eqangle(sk27,sk26,sk27,sk26,sk26,sk26,sk26,sk26),
inference(step,[status(thm)],[t4860,t256]) ).
cnf(t9159,plain,
eqangle(sk27,sk26,sk27,sk26,sk26,sk26,sk26,sk26) = true,
inference(orient,[status(thm)],[t19530]) ).
cnf(t9172,plain,
true = ifeq(cyclic(sk26,sk26,sk27,sk26),true,ifeq(cyclic(sk26,sk26,sk27,sk26),true,ifeq(cyclic(sk26,sk26,sk27,sk26),true,ifeq(true,true,cong(sk26,sk26,sk26,sk26),true),true),true),true),
inference(cp,[status(thm)],[t341,t9159]) ).
cnf(t19531,plain,
true = ifeq(true,true,ifeq(cyclic(sk26,sk26,sk27,sk26),true,ifeq(cyclic(sk26,sk26,sk27,sk26),true,ifeq(true,true,cong(sk26,sk26,sk26,sk26),true),true),true),true),
inference(step,[status(thm)],[t9172,t4857]) ).
cnf(t19532,plain,
true = ifeq(cyclic(sk26,sk26,sk27,sk26),true,ifeq(cyclic(sk26,sk26,sk27,sk26),true,ifeq(true,true,cong(sk26,sk26,sk26,sk26),true),true),true),
inference(step,[status(thm)],[t19531,t256]) ).
cnf(t19533,plain,
true = ifeq(true,true,ifeq(cyclic(sk26,sk26,sk27,sk26),true,ifeq(true,true,cong(sk26,sk26,sk26,sk26),true),true),true),
inference(step,[status(thm)],[t19532,t4857]) ).
cnf(t19534,plain,
true = ifeq(cyclic(sk26,sk26,sk27,sk26),true,ifeq(true,true,cong(sk26,sk26,sk26,sk26),true),true),
inference(step,[status(thm)],[t19533,t256]) ).
cnf(t19535,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk26,sk26,sk26,sk26),true),true),
inference(step,[status(thm)],[t19534,t4857]) ).
cnf(t19536,plain,
true = ifeq(true,true,cong(sk26,sk26,sk26,sk26),true),
inference(step,[status(thm)],[t19535,t256]) ).
cnf(t19537,plain,
true = cong(sk26,sk26,sk26,sk26),
inference(step,[status(thm)],[t19536,t256]) ).
cnf(t9173,plain,
cong(sk26,sk26,sk26,sk26) = true,
inference(orient,[status(thm)],[t19537]) ).
cnf(t9182,plain,
true = ifeq(true,true,ifeq(coll(sk26,sk26,sk26),true,midp(sk26,sk26,sk26),true),true),
inference(cp,[status(thm)],[t327,t9173]) ).
cnf(t19538,plain,
true = ifeq(coll(sk26,sk26,sk26),true,midp(sk26,sk26,sk26),true),
inference(step,[status(thm)],[t9182,t256]) ).
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(t130,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t295,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t130]) ).
cnf(t4505,plain,
true = ifeq(true,true,eqangle(sk26,sk26,sk26,sk27,sk26,sk26,sk26,sk27),true),
inference(cp,[status(thm)],[t343,t4502]) ).
cnf(t19492,plain,
true = eqangle(sk26,sk26,sk26,sk27,sk26,sk26,sk26,sk27),
inference(step,[status(thm)],[t4505,t256]) ).
cnf(t8781,plain,
eqangle(sk26,sk26,sk26,sk27,sk26,sk26,sk26,sk27) = true,
inference(orient,[status(thm)],[t19492]) ).
cnf(t8783,plain,
true = ifeq(true,true,para(sk26,sk26,sk26,sk26),true),
inference(cp,[status(thm)],[t311,t8781]) ).
cnf(t19493,plain,
true = para(sk26,sk26,sk26,sk26),
inference(step,[status(thm)],[t8783,t256]) ).
cnf(t8795,plain,
para(sk26,sk26,sk26,sk26) = true,
inference(orient,[status(thm)],[t19493]) ).
cnf(t8796,plain,
true = ifeq(true,true,coll(sk26,sk26,sk26),true),
inference(cp,[status(thm)],[t295,t8795]) ).
cnf(t19494,plain,
true = coll(sk26,sk26,sk26),
inference(step,[status(thm)],[t8796,t256]) ).
cnf(t8815,plain,
coll(sk26,sk26,sk26) = true,
inference(orient,[status(thm)],[t19494]) ).
cnf(t19539,plain,
true = ifeq(true,true,midp(sk26,sk26,sk26),true),
inference(step,[status(thm)],[t19538,t8815]) ).
cnf(t19540,plain,
true = midp(sk26,sk26,sk26),
inference(step,[status(thm)],[t19539,t256]) ).
cnf(t9211,plain,
midp(sk26,sk26,sk26) = true,
inference(orient,[status(thm)],[t19540]) ).
cnf(t18163,plain,
true = ifeq(true,true,midp(sk26,X1,X1),true),
inference(cp,[status(thm)],[t18162,t9211]) ).
cnf(t20635,plain,
true = midp(sk26,X1,X1),
inference(step,[status(thm)],[t18163,t256]) ).
cnf(t18169,plain,
midp(sk26,X1,X1) = true,
inference(orient,[status(thm)],[t20635]) ).
cnf(t18170,plain,
true = ifeq(true,true,cong(sk26,X1,sk26,X1),true),
inference(cp,[status(thm)],[t363,t18169]) ).
cnf(t20640,plain,
true = cong(sk26,X1,sk26,X1),
inference(step,[status(thm)],[t18170,t256]) ).
cnf(t18316,plain,
cong(sk26,X1,sk26,X1) = true,
inference(orient,[status(thm)],[t20640]) ).
cnf(t18327,plain,
true = ifeq(true,true,ifeq(cong(sk26,X1,sk26,X1),true,perp(sk26,sk26,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t18316]) ).
cnf(t20646,plain,
true = ifeq(cong(sk26,X1,sk26,X1),true,perp(sk26,sk26,X2,X1),true),
inference(step,[status(thm)],[t18327,t256]) ).
cnf(t20647,plain,
true = ifeq(true,true,perp(sk26,sk26,X2,X1),true),
inference(step,[status(thm)],[t20646,t18316]) ).
cnf(t20648,plain,
true = perp(sk26,sk26,X2,X1),
inference(step,[status(thm)],[t20647,t256]) ).
cnf(t18494,plain,
perp(sk26,sk26,X1,X2) = true,
inference(orient,[status(thm)],[t20648]) ).
cnf(t18498,plain,
true = ifeq(true,true,perp(X1,X2,sk26,sk26),true),
inference(cp,[status(thm)],[t274,t18494]) ).
cnf(t20667,plain,
true = perp(X1,X2,sk26,sk26),
inference(step,[status(thm)],[t18498,t256]) ).
cnf(t18785,plain,
perp(X1,X2,sk26,sk26) = true,
inference(orient,[status(thm)],[t20667]) ).
cnf(t18798,plain,
true = ifeq(true,true,ifeq(perp(sk26,sk26,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t18785]) ).
cnf(t20684,plain,
true = ifeq(perp(sk26,sk26,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t18798,t256]) ).
cnf(t20685,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t20684,t18494]) ).
cnf(t20686,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t20685,t256]) ).
cnf(t19153,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t20686]) ).
cnf(c121,plain,
~ para(sk26,sk25,sk27,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk26,sk25,sk27,sk22) != true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t19153]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO611+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Wed Sep 23 12:32:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 61.83/8.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 61.83/8.66 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------