%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO575+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 : n015.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 01:18:11 PM UTC 2026
% Result : Theorem 274.06s 35.39s
% Output : Proof 274.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 78
% Number of leaves : 29
% Syntax : Number of formulae : 348 ( 236 unt; 0 def)
% Number of atoms : 541 ( 230 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 313 ( 120 ~; 114 |; 50 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-4 aty)
% Number of variables : 894 ( 54 sgn 390 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,conjecture,
! [A,B,C,O,H,C1,A1,NWPNT1,NWPNT2] :
( ( coll(A1,A,H)
& circle(O,A,A1,NWPNT2)
& coll(C1,C,H)
& circle(O,C,C1,NWPNT1)
& perp(B,C,A,H)
& perp(A,C,B,H)
& perp(A,B,C,H)
& circle(O,A,B,C) )
=> cong(B,A1,B,C1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL214037) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,H,C1,A1,NWPNT1,NWPNT2] :
( ( coll(A1,A,H)
& circle(O,A,A1,NWPNT2)
& coll(C1,C,H)
& circle(O,C,C1,NWPNT1)
& perp(B,C,A,H)
& perp(A,C,B,H)
& perp(A,B,C,H)
& circle(O,A,B,C) )
=> cong(B,A1,B,C1) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,H,C1,A1,NWPNT1,NWPNT2] :
( ~ cong(B,A1,B,C1)
& coll(A1,A,H)
& circle(O,A,A1,NWPNT2)
& coll(C1,C,H)
& circle(O,C,C1,NWPNT1)
& perp(B,C,A,H)
& perp(A,C,B,H)
& perp(A,B,C,H)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cong(sk21,sk26,sk21,sk25)
& coll(sk26,sk20,sk24)
& circle(sk23,sk20,sk26,sk28)
& coll(sk25,sk22,sk24)
& circle(sk23,sk22,sk25,sk27)
& perp(sk21,sk22,sk20,sk24)
& perp(sk20,sk22,sk21,sk24)
& perp(sk20,sk21,sk22,sk24)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28])],[f94_nnf]) ).
cnf(c121,plain,
~ cong(sk21,sk26,sk21,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t16,plain,
cong(sk21,sk26,sk21,sk25) = false,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(t3078,plain,
cong(sk21,sk26,sk21,sk25) = false,
inference(orient,[status(thm)],[t16]) ).
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(t97,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)],[t97]) ).
cnf(t3080,plain,
true = ifeq(midp(sk21,sk26,sk25),true,false,true),
inference(cp,[status(thm)],[t363,t3078]) ).
cnf(t7167,plain,
ifeq(midp(sk21,sk26,sk25),true,false,true) = true,
inference(orient,[status(thm)],[t3080]) ).
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(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(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(t188,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)],[t188]) ).
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(t112,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)],[t112]) ).
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(t175,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)],[t175]) ).
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(t142,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)],[t142]) ).
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(t180,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)],[t180]) ).
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(t143,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)],[t143]) ).
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,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
perp(sk20,sk21,sk22,sk24) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h1,plain,
perp(sk22,sk24,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(t34,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi114,h1]) ).
cnf(t1671,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t1674,plain,
true = ifeq(true,true,eqangle(sk20,sk21,X1,X2,sk20,sk21,X1,X2),true),
inference(cp,[status(thm)],[t294,t1671]) ).
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(t60837,plain,
true = eqangle(sk20,sk21,X1,X2,sk20,sk21,X1,X2),
inference(step,[status(thm)],[t1674,t256]) ).
cnf(t16404,plain,
eqangle(sk20,sk21,X1,X2,sk20,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t60837]) ).
cnf(t16410,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk21,X1,X2,sk20,sk21),true),
inference(cp,[status(thm)],[t305,t16404]) ).
cnf(t61399,plain,
true = eqangle(X1,X2,sk20,sk21,X1,X2,sk20,sk21),
inference(step,[status(thm)],[t16410,t256]) ).
cnf(t23478,plain,
eqangle(X1,X2,sk20,sk21,X1,X2,sk20,sk21) = true,
inference(orient,[status(thm)],[t61399]) ).
cnf(t23480,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t311,t23478]) ).
cnf(t61400,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t23480,t256]) ).
cnf(t23499,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t61400]) ).
cnf(t23515,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,t23499]) ).
cnf(t64311,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)],[t23515,t256]) ).
cnf(t64312,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t64311,t23499]) ).
cnf(t64313,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t64312,t256]) ).
cnf(t56762,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t64313]) ).
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(t166,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)],[t166]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t104,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t323,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t104]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t105,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t321,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t105]) ).
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(t141,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)],[t141]) ).
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(t107,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)],[t107]) ).
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(c120,plain,
coll(sk26,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
coll(sk26,sk20,sk24) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h20,plain,
coll(sk24,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi120,hi120]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD7) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(c115,plain,
perp(sk20,sk22,sk21,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
perp(sk20,sk22,sk21,sk24) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h4,plain,
perp(sk20,sk22,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi115]) ).
cnf(h3,plain,
perp(sk21,sk24,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi115]) ).
cnf(h35,plain,
para(sk21,sk24,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h3,h4]) ).
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(h136,plain,
eqangle(sk21,sk24,V0,V1,sk24,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h35]) ).
fof(f17,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD18) ).
fof(f17_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X1,X0,X2,X3,X4,X5,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h546,plain,
eqangle(sk24,sk21,V0,V1,sk24,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi17,h136]) ).
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(t25,plain,
cyclic(sk21,sk26,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi42,h546,h20]) ).
cnf(t2498,plain,
cyclic(sk21,sk26,sk24,sk24) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t2499,plain,
true = ifeq(true,true,cyclic(sk21,sk24,sk26,sk24),true),
inference(cp,[status(thm)],[t346,t2498]) ).
cnf(t60303,plain,
true = cyclic(sk21,sk24,sk26,sk24),
inference(step,[status(thm)],[t2499,t256]) ).
cnf(t4408,plain,
cyclic(sk21,sk24,sk26,sk24) = true,
inference(orient,[status(thm)],[t60303]) ).
cnf(t4413,plain,
true = ifeq(true,true,eqangle(sk26,sk21,sk26,sk24,sk24,sk21,sk24,sk24),true),
inference(cp,[status(thm)],[t343,t4408]) ).
cnf(t61062,plain,
true = eqangle(sk26,sk21,sk26,sk24,sk24,sk21,sk24,sk24),
inference(step,[status(thm)],[t4413,t256]) ).
cnf(t19695,plain,
eqangle(sk26,sk21,sk26,sk24,sk24,sk21,sk24,sk24) = true,
inference(orient,[status(thm)],[t61062]) ).
cnf(t19711,plain,
true = ifeq(cyclic(sk21,sk24,sk26,sk21),true,ifeq(cyclic(sk21,sk24,sk26,sk24),true,ifeq(cyclic(sk21,sk24,sk26,sk24),true,ifeq(true,true,cong(sk21,sk24,sk21,sk24),true),true),true),true),
inference(cp,[status(thm)],[t341,t19695]) ).
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(t108,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)],[t108]) ).
cnf(h33,plain,
para(sk21,sk24,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi8,h3,hi115]) ).
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(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h125,plain,
coll(sk21,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi66,h33]) ).
cnf(h425,plain,
coll(sk24,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h125,h125]) ).
cnf(h1053,plain,
coll(sk26,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h20,h425]) ).
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(h3491,plain,
coll(sk26,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1053]) ).
cnf(h7007,plain,
coll(sk21,sk21,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h3491,h3491]) ).
cnf(h126,plain,
eqangle(sk21,sk24,V0,V1,sk21,sk24,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h33]) ).
cnf(t31,plain,
cyclic(sk24,sk26,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h126,h7007]) ).
cnf(t2610,plain,
cyclic(sk24,sk26,sk21,sk21) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t2611,plain,
true = ifeq(true,true,cyclic(sk24,sk21,sk26,sk21),true),
inference(cp,[status(thm)],[t346,t2610]) ).
cnf(t60314,plain,
true = cyclic(sk24,sk21,sk26,sk21),
inference(step,[status(thm)],[t2611,t256]) ).
cnf(t4601,plain,
cyclic(sk24,sk21,sk26,sk21) = true,
inference(orient,[status(thm)],[t60314]) ).
cnf(t4604,plain,
true = ifeq(true,true,cyclic(sk21,sk24,sk26,sk21),true),
inference(cp,[status(thm)],[t344,t4601]) ).
cnf(t60363,plain,
true = cyclic(sk21,sk24,sk26,sk21),
inference(step,[status(thm)],[t4604,t256]) ).
cnf(t5627,plain,
cyclic(sk21,sk24,sk26,sk21) = true,
inference(orient,[status(thm)],[t60363]) ).
cnf(t61063,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk24,sk26,sk24),true,ifeq(cyclic(sk21,sk24,sk26,sk24),true,ifeq(true,true,cong(sk21,sk24,sk21,sk24),true),true),true),true),
inference(step,[status(thm)],[t19711,t5627]) ).
cnf(t61064,plain,
true = ifeq(cyclic(sk21,sk24,sk26,sk24),true,ifeq(cyclic(sk21,sk24,sk26,sk24),true,ifeq(true,true,cong(sk21,sk24,sk21,sk24),true),true),true),
inference(step,[status(thm)],[t61063,t256]) ).
cnf(t61065,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk24,sk26,sk24),true,ifeq(true,true,cong(sk21,sk24,sk21,sk24),true),true),true),
inference(step,[status(thm)],[t61064,t4408]) ).
cnf(t61066,plain,
true = ifeq(cyclic(sk21,sk24,sk26,sk24),true,ifeq(true,true,cong(sk21,sk24,sk21,sk24),true),true),
inference(step,[status(thm)],[t61065,t256]) ).
cnf(t61067,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk24,sk21,sk24),true),true),
inference(step,[status(thm)],[t61066,t4408]) ).
cnf(t61068,plain,
true = ifeq(true,true,cong(sk21,sk24,sk21,sk24),true),
inference(step,[status(thm)],[t61067,t256]) ).
cnf(t61069,plain,
true = cong(sk21,sk24,sk21,sk24),
inference(step,[status(thm)],[t61068,t256]) ).
cnf(t19712,plain,
cong(sk21,sk24,sk21,sk24) = true,
inference(orient,[status(thm)],[t61069]) ).
cnf(t19715,plain,
true = ifeq(true,true,cong(sk21,sk24,sk24,sk21),true),
inference(cp,[status(thm)],[t323,t19712]) ).
cnf(t61073,plain,
true = cong(sk21,sk24,sk24,sk21),
inference(step,[status(thm)],[t19715,t256]) ).
cnf(t19780,plain,
cong(sk21,sk24,sk24,sk21) = true,
inference(orient,[status(thm)],[t61073]) ).
cnf(t19782,plain,
true = ifeq(true,true,cong(sk24,sk21,sk21,sk24),true),
inference(cp,[status(thm)],[t321,t19780]) ).
cnf(t61074,plain,
true = cong(sk24,sk21,sk21,sk24),
inference(step,[status(thm)],[t19782,t256]) ).
cnf(t19790,plain,
cong(sk24,sk21,sk21,sk24) = true,
inference(orient,[status(thm)],[t61074]) ).
cnf(t19792,plain,
true = ifeq(true,true,cong(sk24,sk21,sk24,sk21),true),
inference(cp,[status(thm)],[t323,t19790]) ).
cnf(t61075,plain,
true = cong(sk24,sk21,sk24,sk21),
inference(step,[status(thm)],[t19792,t256]) ).
cnf(t19799,plain,
cong(sk24,sk21,sk24,sk21) = true,
inference(orient,[status(thm)],[t61075]) ).
cnf(t19808,plain,
true = ifeq(true,true,ifeq(coll(sk24,sk21,sk21),true,midp(sk24,sk21,sk21),true),true),
inference(cp,[status(thm)],[t327,t19799]) ).
cnf(t61076,plain,
true = ifeq(coll(sk24,sk21,sk21),true,midp(sk24,sk21,sk21),true),
inference(step,[status(thm)],[t19808,t256]) ).
cnf(t98,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)],[t98]) ).
cnf(h36,plain,
perp(sk24,sk21,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,h4]) ).
cnf(t41,plain,
para(sk24,sk21,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,h36,h4]) ).
cnf(t1925,plain,
para(sk24,sk21,sk24,sk21) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t1927,plain,
true = ifeq(true,true,coll(sk24,sk21,sk21),true),
inference(cp,[status(thm)],[t295,t1925]) ).
cnf(t60257,plain,
true = coll(sk24,sk21,sk21),
inference(step,[status(thm)],[t1927,t256]) ).
cnf(t3339,plain,
coll(sk24,sk21,sk21) = true,
inference(orient,[status(thm)],[t60257]) ).
cnf(t61077,plain,
true = ifeq(true,true,midp(sk24,sk21,sk21),true),
inference(step,[status(thm)],[t61076,t3339]) ).
cnf(t61078,plain,
true = midp(sk24,sk21,sk21),
inference(step,[status(thm)],[t61077,t256]) ).
cnf(t19838,plain,
midp(sk24,sk21,sk21) = true,
inference(orient,[status(thm)],[t61078]) ).
cnf(t56763,plain,
true = ifeq(true,true,midp(sk24,X1,X1),true),
inference(cp,[status(thm)],[t56762,t19838]) ).
cnf(t64314,plain,
true = midp(sk24,X1,X1),
inference(step,[status(thm)],[t56763,t256]) ).
cnf(t56767,plain,
midp(sk24,X1,X1) = true,
inference(orient,[status(thm)],[t64314]) ).
cnf(t56768,plain,
true = ifeq(true,true,cong(sk24,X1,sk24,X1),true),
inference(cp,[status(thm)],[t363,t56767]) ).
cnf(t64317,plain,
true = cong(sk24,X1,sk24,X1),
inference(step,[status(thm)],[t56768,t256]) ).
cnf(t56827,plain,
cong(sk24,X1,sk24,X1) = true,
inference(orient,[status(thm)],[t64317]) ).
cnf(t56838,plain,
true = ifeq(true,true,ifeq(cong(sk24,X1,sk24,X1),true,perp(sk24,sk24,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t56827]) ).
cnf(t64321,plain,
true = ifeq(cong(sk24,X1,sk24,X1),true,perp(sk24,sk24,X2,X1),true),
inference(step,[status(thm)],[t56838,t256]) ).
cnf(t64322,plain,
true = ifeq(true,true,perp(sk24,sk24,X2,X1),true),
inference(step,[status(thm)],[t64321,t56827]) ).
cnf(t64323,plain,
true = perp(sk24,sk24,X2,X1),
inference(step,[status(thm)],[t64322,t256]) ).
cnf(t56945,plain,
perp(sk24,sk24,X1,X2) = true,
inference(orient,[status(thm)],[t64323]) ).
cnf(t56952,plain,
true = ifeq(true,true,perp(X1,X2,sk24,sk24),true),
inference(cp,[status(thm)],[t274,t56945]) ).
cnf(t64336,plain,
true = perp(X1,X2,sk24,sk24),
inference(step,[status(thm)],[t56952,t256]) ).
cnf(t57184,plain,
perp(X1,X2,sk24,sk24) = true,
inference(orient,[status(thm)],[t64336]) ).
cnf(t57201,plain,
true = ifeq(true,true,ifeq(perp(sk24,sk24,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t57184]) ).
cnf(t64364,plain,
true = ifeq(perp(sk24,sk24,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t57201,t256]) ).
cnf(t64365,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t64364,t56945]) ).
cnf(t64366,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t64365,t256]) ).
cnf(t58141,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t64366]) ).
cnf(t64408,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(step,[status(thm)],[t353,t58141]) ).
cnf(t64409,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t64408,t256]) ).
cnf(t64410,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t64409,t58141]) ).
cnf(t64411,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t64410,t256]) ).
cnf(t58168,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t64411]) ).
cnf(t60223,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t58168]) ).
cnf(h22,plain,
coll(sk26,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi120]) ).
cnf(h84,plain,
coll(sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h22,h22]) ).
cnf(h25,plain,
para(sk20,sk21,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi114,h1]) ).
cnf(h93,plain,
eqangle(sk20,sk21,V0,V1,sk20,sk21,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h25]) ).
cnf(h332,plain,
cyclic(sk21,sk26,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h93,h84]) ).
cnf(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t19,plain,
cyclic(sk21,sk20,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h332]) ).
cnf(t2424,plain,
cyclic(sk21,sk20,sk26,sk20) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t2431,plain,
true = ifeq(true,true,eqangle(sk26,sk21,sk26,sk20,sk20,sk21,sk20,sk20),true),
inference(cp,[status(thm)],[t343,t2424]) ).
cnf(t60845,plain,
true = eqangle(sk26,sk21,sk26,sk20,sk20,sk21,sk20,sk20),
inference(step,[status(thm)],[t2431,t256]) ).
cnf(t16545,plain,
eqangle(sk26,sk21,sk26,sk20,sk20,sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t60845]) ).
cnf(t16561,plain,
true = ifeq(cyclic(sk21,sk20,sk26,sk21),true,ifeq(cyclic(sk21,sk20,sk26,sk20),true,ifeq(cyclic(sk21,sk20,sk26,sk20),true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),true),true),
inference(cp,[status(thm)],[t341,t16545]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD14) ).
fof(f13_nnf,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t106,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t348,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t106]) ).
cnf(h1059,plain,
coll(sk21,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h425,h20]) ).
cnf(h3709,plain,
coll(sk21,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1059]) ).
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(c97,plain,
( coll(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(hi97,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X1,X0,X3),true,coll(sk10(X0,X2,X3,X1),X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c97]) ).
cnf(c116,plain,
perp(sk21,sk22,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
perp(sk21,sk22,sk20,sk24) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h7,plain,
coll(sk10(sk20,sk21,sk24,sk22),sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi97,hi115,hi116]) ).
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]) ).
cnf(h44,plain,
coll(sk24,sk10(sk20,sk21,sk24,sk22),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi1,h7]) ).
cnf(h168,plain,
coll(sk20,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h44,h44]) ).
cnf(h92,plain,
coll(sk20,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi66,h25]) ).
cnf(h253,plain,
coll(sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h92,h92]) ).
cnf(h801,plain,
coll(sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h253,h253]) ).
cnf(h2360,plain,
coll(sk21,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h801,h168]) ).
cnf(h7473,plain,
coll(sk20,sk26,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2360,h3709]) ).
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(hi20,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X0,X1,X4,X5,X2,X3,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h336,plain,
eqangle(sk20,sk21,sk20,sk21,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h93]) ).
cnf(t21,plain,
cyclic(sk21,sk21,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi42,h336,h7473]) ).
cnf(t2444,plain,
cyclic(sk21,sk21,sk20,sk26) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t2447,plain,
true = ifeq(true,true,cyclic(sk21,sk20,sk21,sk26),true),
inference(cp,[status(thm)],[t346,t2444]) ).
cnf(t60300,plain,
true = cyclic(sk21,sk20,sk21,sk26),
inference(step,[status(thm)],[t2447,t256]) ).
cnf(t4353,plain,
cyclic(sk21,sk20,sk21,sk26) = true,
inference(orient,[status(thm)],[t60300]) ).
cnf(t4354,plain,
true = ifeq(true,true,cyclic(sk21,sk20,sk26,sk21),true),
inference(cp,[status(thm)],[t348,t4353]) ).
cnf(t60341,plain,
true = cyclic(sk21,sk20,sk26,sk21),
inference(step,[status(thm)],[t4354,t256]) ).
cnf(t5240,plain,
cyclic(sk21,sk20,sk26,sk21) = true,
inference(orient,[status(thm)],[t60341]) ).
cnf(t60846,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk20,sk26,sk20),true,ifeq(cyclic(sk21,sk20,sk26,sk20),true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),true),true),
inference(step,[status(thm)],[t16561,t5240]) ).
cnf(t60847,plain,
true = ifeq(cyclic(sk21,sk20,sk26,sk20),true,ifeq(cyclic(sk21,sk20,sk26,sk20),true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),true),
inference(step,[status(thm)],[t60846,t256]) ).
cnf(t60848,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk20,sk26,sk20),true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),true),
inference(step,[status(thm)],[t60847,t2424]) ).
cnf(t60849,plain,
true = ifeq(cyclic(sk21,sk20,sk26,sk20),true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),
inference(step,[status(thm)],[t60848,t256]) ).
cnf(t60850,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),true),
inference(step,[status(thm)],[t60849,t2424]) ).
cnf(t60851,plain,
true = ifeq(true,true,cong(sk21,sk20,sk21,sk20),true),
inference(step,[status(thm)],[t60850,t256]) ).
cnf(t60852,plain,
true = cong(sk21,sk20,sk21,sk20),
inference(step,[status(thm)],[t60851,t256]) ).
cnf(t16562,plain,
cong(sk21,sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t60852]) ).
cnf(t16573,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk20,sk20),true,midp(sk21,sk20,sk20),true),true),
inference(cp,[status(thm)],[t327,t16562]) ).
cnf(t60853,plain,
true = ifeq(coll(sk21,sk20,sk20),true,midp(sk21,sk20,sk20),true),
inference(step,[status(thm)],[t16573,t256]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t109,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t292,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t109]) ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD5) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t110,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t290,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t110]) ).
cnf(hi3,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t35,plain,
para(sk20,sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi3,h25]) ).
cnf(t1700,plain,
para(sk20,sk21,sk21,sk20) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t1703,plain,
true = ifeq(true,true,para(sk21,sk20,sk20,sk21),true),
inference(cp,[status(thm)],[t290,t1700]) ).
cnf(t60278,plain,
true = para(sk21,sk20,sk20,sk21),
inference(step,[status(thm)],[t1703,t256]) ).
cnf(t3957,plain,
para(sk21,sk20,sk20,sk21) = true,
inference(orient,[status(thm)],[t60278]) ).
cnf(t3960,plain,
true = ifeq(true,true,para(sk21,sk20,sk21,sk20),true),
inference(cp,[status(thm)],[t292,t3957]) ).
cnf(t60328,plain,
true = para(sk21,sk20,sk21,sk20),
inference(step,[status(thm)],[t3960,t256]) ).
cnf(t4894,plain,
para(sk21,sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t60328]) ).
cnf(t4896,plain,
true = ifeq(true,true,coll(sk21,sk20,sk20),true),
inference(cp,[status(thm)],[t295,t4894]) ).
cnf(t60329,plain,
true = coll(sk21,sk20,sk20),
inference(step,[status(thm)],[t4896,t256]) ).
cnf(t4921,plain,
coll(sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t60329]) ).
cnf(t60854,plain,
true = ifeq(true,true,midp(sk21,sk20,sk20),true),
inference(step,[status(thm)],[t60853,t4921]) ).
cnf(t60855,plain,
true = midp(sk21,sk20,sk20),
inference(step,[status(thm)],[t60854,t256]) ).
cnf(t16603,plain,
midp(sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t60855]) ).
cnf(t56764,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t56762,t16603]) ).
cnf(t64315,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t56764,t256]) ).
cnf(t56787,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t64315]) ).
cnf(t60225,plain,
true = ifeq(true,true,midp(sk21,X1,X2),true),
inference(cp,[status(thm)],[t60223,t56787]) ).
cnf(t64587,plain,
true = midp(sk21,X1,X2),
inference(step,[status(thm)],[t60225,t256]) ).
cnf(t60233,plain,
midp(sk21,X1,X2) = true,
inference(orient,[status(thm)],[t64587]) ).
cnf(t64590,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t7167,t60233]) ).
cnf(t64591,plain,
false = true,
inference(step,[status(thm)],[t64590,t256]) ).
cnf(t60240,plain,
false = true,
inference(rw,[status(thm)],[t64591]) ).
cnf(t60241,plain,
false = true,
inference(orient,[status(thm)],[t60240]) ).
cnf(t64592,plain,
cong(sk21,sk26,sk21,sk25) = true,
inference(step,[status(thm)],[t3078,t60241]) ).
cnf(t60242,plain,
cong(sk21,sk26,sk21,sk25) = true,
inference(orient,[status(thm)],[t64592]) ).
cnf(goal_0,negated_conjecture,
cong(sk21,sk26,sk21,sk25) != true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t60242]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO575+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 12:30:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 274.06/35.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 274.06/35.39 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------