%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO660+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 : n009.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 01:18:25 PM UTC 2026
% Result : Theorem 168.78s 21.84s
% Output : Proof 168.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 20
% Syntax : Number of formulae : 207 ( 131 unt; 0 def)
% Number of atoms : 368 ( 126 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 254 ( 93 ~; 87 |; 54 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 601 ( 32 sgn 257 !; 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(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)],[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(t136,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)],[t136]) ).
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(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)],[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(t125,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)],[t125]) ).
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(t224,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)],[t224]) ).
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(t154,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)],[t154]) ).
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(t181,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)],[t181]) ).
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(t155,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)],[t155]) ).
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] :
( ( coll(G,A,E)
& coll(G,B,C)
& eqangle(D,C,C,F,F,C,C,B)
& eqangle(B,A,A,E,E,A,A,C)
& coll(F,A,B)
& coll(E,C,D)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(C,A,C,B) )
=> para(E,F,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo7Book00EE02E02319) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( coll(G,A,E)
& coll(G,B,C)
& eqangle(D,C,C,F,F,C,C,B)
& eqangle(B,A,A,E,E,A,A,C)
& coll(F,A,B)
& coll(E,C,D)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(C,A,C,B) )
=> para(E,F,C,B) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G] :
( ~ para(E,F,C,B)
& coll(G,A,E)
& coll(G,B,C)
& eqangle(D,C,C,F,F,C,C,B)
& eqangle(B,A,A,E,E,A,A,C)
& coll(F,A,B)
& coll(E,C,D)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(C,A,C,B) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk24,sk25,sk22,sk21)
& coll(sk26,sk20,sk24)
& coll(sk26,sk21,sk22)
& eqangle(sk23,sk22,sk22,sk25,sk25,sk22,sk22,sk21)
& eqangle(sk21,sk20,sk20,sk24,sk24,sk20,sk20,sk22)
& coll(sk25,sk20,sk21)
& coll(sk24,sk22,sk23)
& 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])],[f94_nnf]) ).
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(t28,plain,
para(sk22,sk21,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h4,hi113]) ).
cnf(t1750,plain,
para(sk22,sk21,sk22,sk21) = true,
inference(orient,[status(thm)],[t28]) ).
cnf(t1753,plain,
true = ifeq(true,true,eqangle(sk22,sk21,X1,X2,sk22,sk21,X1,X2),true),
inference(cp,[status(thm)],[t294,t1750]) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t24]) ).
cnf(t30047,plain,
true = eqangle(sk22,sk21,X1,X2,sk22,sk21,X1,X2),
inference(step,[status(thm)],[t1753,t256]) ).
cnf(t8046,plain,
eqangle(sk22,sk21,X1,X2,sk22,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t30047]) ).
cnf(t8053,plain,
true = ifeq(true,true,eqangle(X1,X2,sk22,sk21,X1,X2,sk22,sk21),true),
inference(cp,[status(thm)],[t305,t8046]) ).
cnf(t30405,plain,
true = eqangle(X1,X2,sk22,sk21,X1,X2,sk22,sk21),
inference(step,[status(thm)],[t8053,t256]) ).
cnf(t12724,plain,
eqangle(X1,X2,sk22,sk21,X1,X2,sk22,sk21) = true,
inference(orient,[status(thm)],[t30405]) ).
cnf(t12726,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t311,t12724]) ).
cnf(t30406,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t12726,t256]) ).
cnf(t12747,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t30406]) ).
cnf(t12763,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,t12747]) ).
cnf(t32185,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)],[t12763,t256]) ).
cnf(t32186,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t32185,t12747]) ).
cnf(t32187,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t32186,t256]) ).
cnf(t29337,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t32187]) ).
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(t160,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)],[t160]) ).
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(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/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(t153,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)],[t153]) ).
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(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c116,plain,
coll(sk24,sk22,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk24,sk22,sk23) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h13,plain,
coll(sk24,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi116]) ).
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(h65,plain,
coll(sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h13,h13]) ).
cnf(h50,plain,
para(sk22,sk21,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h4,hi113]) ).
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(h179,plain,
eqangle(sk22,sk21,V0,V1,sk22,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h50]) ).
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(h887,plain,
cyclic(sk21,sk24,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h179,h65]) ).
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(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t16,plain,
cyclic(sk21,sk22,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi14,h887]) ).
cnf(t2509,plain,
cyclic(sk21,sk22,sk24,sk22) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t2516,plain,
true = ifeq(true,true,eqangle(sk24,sk21,sk24,sk22,sk22,sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t343,t2509]) ).
cnf(t30081,plain,
true = eqangle(sk24,sk21,sk24,sk22,sk22,sk21,sk22,sk22),
inference(step,[status(thm)],[t2516,t256]) ).
cnf(t8519,plain,
eqangle(sk24,sk21,sk24,sk22,sk22,sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t30081]) ).
cnf(t8535,plain,
true = ifeq(cyclic(sk21,sk22,sk24,sk21),true,ifeq(cyclic(sk21,sk22,sk24,sk22),true,ifeq(cyclic(sk21,sk22,sk24,sk22),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),true),
inference(cp,[status(thm)],[t341,t8519]) ).
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(t132,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)],[t132]) ).
cnf(t131,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)],[t131]) ).
cnf(c115,plain,
coll(sk23,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
coll(sk23,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h8,plain,
coll(sk21,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi115,hi115]) ).
cnf(h33,plain,
coll(sk23,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h8,h8]) ).
cnf(h11,plain,
coll(sk23,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi116,hi116]) ).
cnf(h122,plain,
coll(sk24,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h11,h33]) ).
cnf(h393,plain,
coll(sk24,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h122]) ).
cnf(h1948,plain,
coll(sk21,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h393,h393]) ).
fof(f85,axiom,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,H,A,C)
& perp(A,H,B,C) )
=> ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX10) ).
fof(f85_nnf,plain,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(nnf_transformation,[status(thm)],[f85]) ).
fof(f85_sk,plain,
! [A,H,B,C] :
( ( perp(B,sk10(A,B,C,H),C,A)
& coll(sk10(A,B,C,H),C,A)
& perp(A,sk9(A,B,C,H),C,B)
& coll(sk9(A,B,C,H),C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f85_nnf]) ).
cnf(c98,plain,
( perp(X1,sk10(X0,X1,X2,X3),X2,X0)
| ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(hi98,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X1,X0,X3),true,perp(X2,sk10(X0,X2,X3,X1),X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c98]) ).
cnf(h0,plain,
perp(sk22,sk10(sk22,sk22,sk21,sk20),sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi98,hi113,hi113]) ).
cnf(h31,plain,
perp(sk21,sk22,sk22,sk10(sk22,sk22,sk21,sk20)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
cnf(h113,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,h31,h0]) ).
cnf(h407,plain,
eqangle(sk21,sk22,V0,V1,sk21,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h113]) ).
cnf(t20,plain,
cyclic(sk22,sk24,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h407,h1948]) ).
cnf(t2490,plain,
cyclic(sk22,sk24,sk21,sk21) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t2491,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk24,sk21),true),
inference(cp,[status(thm)],[t346,t2490]) ).
cnf(t29866,plain,
true = cyclic(sk22,sk21,sk24,sk21),
inference(step,[status(thm)],[t2491,t256]) ).
cnf(t4467,plain,
cyclic(sk22,sk21,sk24,sk21) = true,
inference(orient,[status(thm)],[t29866]) ).
cnf(t4470,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk24,sk21),true),
inference(cp,[status(thm)],[t344,t4467]) ).
cnf(t29892,plain,
true = cyclic(sk21,sk22,sk24,sk21),
inference(step,[status(thm)],[t4470,t256]) ).
cnf(t4968,plain,
cyclic(sk21,sk22,sk24,sk21) = true,
inference(orient,[status(thm)],[t29892]) ).
cnf(t30082,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk22,sk24,sk22),true,ifeq(cyclic(sk21,sk22,sk24,sk22),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),true),
inference(step,[status(thm)],[t8535,t4968]) ).
cnf(t30083,plain,
true = ifeq(cyclic(sk21,sk22,sk24,sk22),true,ifeq(cyclic(sk21,sk22,sk24,sk22),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),
inference(step,[status(thm)],[t30082,t256]) ).
cnf(t30084,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk22,sk24,sk22),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),
inference(step,[status(thm)],[t30083,t2509]) ).
cnf(t30085,plain,
true = ifeq(cyclic(sk21,sk22,sk24,sk22),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),
inference(step,[status(thm)],[t30084,t256]) ).
cnf(t30086,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),
inference(step,[status(thm)],[t30085,t2509]) ).
cnf(t30087,plain,
true = ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),
inference(step,[status(thm)],[t30086,t256]) ).
cnf(t30088,plain,
true = cong(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t30087,t256]) ).
cnf(t8536,plain,
cong(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t30088]) ).
cnf(t8547,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk22,sk22),true,midp(sk21,sk22,sk22),true),true),
inference(cp,[status(thm)],[t327,t8536]) ).
cnf(t30089,plain,
true = ifeq(coll(sk21,sk22,sk22),true,midp(sk21,sk22,sk22),true),
inference(step,[status(thm)],[t8547,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(t126,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)],[t126]) ).
cnf(t25,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,h31,h0]) ).
cnf(t2121,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t2123,plain,
true = ifeq(true,true,coll(sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t295,t2121]) ).
cnf(t29834,plain,
true = coll(sk21,sk22,sk22),
inference(step,[status(thm)],[t2123,t256]) ).
cnf(t3541,plain,
coll(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t29834]) ).
cnf(t30090,plain,
true = ifeq(true,true,midp(sk21,sk22,sk22),true),
inference(step,[status(thm)],[t30089,t3541]) ).
cnf(t30091,plain,
true = midp(sk21,sk22,sk22),
inference(step,[status(thm)],[t30090,t256]) ).
cnf(t8577,plain,
midp(sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t30091]) ).
cnf(t29338,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t29337,t8577]) ).
cnf(t32188,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t29338,t256]) ).
cnf(t29340,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t32188]) ).
cnf(t29341,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X1),true),
inference(cp,[status(thm)],[t363,t29340]) ).
cnf(t32190,plain,
true = cong(sk21,X1,sk21,X1),
inference(step,[status(thm)],[t29341,t256]) ).
cnf(t29384,plain,
cong(sk21,X1,sk21,X1) = true,
inference(orient,[status(thm)],[t32190]) ).
cnf(t29395,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t29384]) ).
cnf(t32193,plain,
true = ifeq(cong(sk21,X1,sk21,X1),true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t29395,t256]) ).
cnf(t32194,plain,
true = ifeq(true,true,perp(sk21,sk21,X2,X1),true),
inference(step,[status(thm)],[t32193,t29384]) ).
cnf(t32195,plain,
true = perp(sk21,sk21,X2,X1),
inference(step,[status(thm)],[t32194,t256]) ).
cnf(t29472,plain,
perp(sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t32195]) ).
cnf(t29475,plain,
true = ifeq(true,true,perp(X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t274,t29472]) ).
cnf(t32206,plain,
true = perp(X1,X2,sk21,sk21),
inference(step,[status(thm)],[t29475,t256]) ).
cnf(t29599,plain,
perp(X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t32206]) ).
cnf(t29613,plain,
true = ifeq(true,true,ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t29599]) ).
cnf(t32216,plain,
true = ifeq(perp(sk21,sk21,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t29613,t256]) ).
cnf(t32217,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t32216,t29472]) ).
cnf(t32218,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t32217,t256]) ).
cnf(t29800,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t32218]) ).
cnf(c122,plain,
~ para(sk24,sk25,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk24,sk25,sk22,sk21) != true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t29800]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO660+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.38 % Computer : n009.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 12:41:44 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 168.78/21.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 168.78/21.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------