%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO609+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 : n016.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 115.46s 16.92s
% Output : Proof 115.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 29
% Syntax : Number of formulae : 291 ( 179 unt; 0 def)
% Number of atoms : 475 ( 173 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 307 ( 123 ~; 117 |; 38 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-4 aty)
% Number of variables : 902 ( 32 sgn 424 !; 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(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(t260,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/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(t135,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t269,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t135]) ).
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(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/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(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/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(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/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(t157,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)],[t157]) ).
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(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/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(t158,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)],[t158]) ).
fof(f86,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX11) ).
fof(f86_nnf,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f86]) ).
fof(f86_sk,plain,
! [O,A,B,C] :
( perp(sk11(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f86_nnf]) ).
cnf(c99,plain,
( perp(sk11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f86_sk]) ).
cnf(hi99,axiom,
ifeq(circle(X0,X1,X2,X3),true,perp(sk11(X1,X2,X3,X0),X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
fof(f94,conjecture,
! [A,B,C,O,E,F,G,NWPNT1] :
( ( coll(G,A,C)
& perp(G,E,A,C)
& coll(F,A,B)
& perp(F,E,A,B)
& circle(O,A,E,NWPNT1)
& para(B,C,E,A)
& circle(O,A,B,C) )
=> para(F,G,A,O) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618071) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,E,F,G,NWPNT1] :
( ( coll(G,A,C)
& perp(G,E,A,C)
& coll(F,A,B)
& perp(F,E,A,B)
& circle(O,A,E,NWPNT1)
& para(B,C,E,A)
& circle(O,A,B,C) )
=> para(F,G,A,O) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,E,F,G,NWPNT1] :
( ~ para(F,G,A,O)
& coll(G,A,C)
& perp(G,E,A,C)
& coll(F,A,B)
& perp(F,E,A,B)
& circle(O,A,E,NWPNT1)
& para(B,C,E,A)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk25,sk26,sk20,sk23)
& coll(sk26,sk20,sk22)
& perp(sk26,sk24,sk20,sk22)
& coll(sk25,sk20,sk21)
& perp(sk25,sk24,sk20,sk21)
& circle(sk23,sk20,sk24,sk27)
& para(sk21,sk22,sk24,sk20)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c113,plain,
circle(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
circle(sk23,sk20,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
perp(sk11(sk20,sk21,sk22,sk23),sk20,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi113]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h15,plain,
perp(sk20,sk23,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
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(t30,plain,
para(sk20,sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi8,h15,h0]) ).
cnf(t1593,plain,
para(sk20,sk23,sk20,sk23) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t1596,plain,
true = ifeq(true,true,eqangle(sk20,sk23,X1,X2,sk20,sk23,X1,X2),true),
inference(cp,[status(thm)],[t294,t1593]) ).
cnf(t29,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t29]) ).
cnf(t19525,plain,
true = eqangle(sk20,sk23,X1,X2,sk20,sk23,X1,X2),
inference(step,[status(thm)],[t1596,t256]) ).
cnf(t5446,plain,
eqangle(sk20,sk23,X1,X2,sk20,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t19525]) ).
cnf(t5453,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk23,X1,X2,sk20,sk23),true),
inference(cp,[status(thm)],[t305,t5446]) ).
cnf(t19829,plain,
true = eqangle(X1,X2,sk20,sk23,X1,X2,sk20,sk23),
inference(step,[status(thm)],[t5453,t256]) ).
cnf(t9179,plain,
eqangle(X1,X2,sk20,sk23,X1,X2,sk20,sk23) = true,
inference(orient,[status(thm)],[t19829]) ).
cnf(t9182,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t311,t9179]) ).
cnf(t19830,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t9182,t256]) ).
cnf(t9203,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t19830]) ).
cnf(t9219,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,t9203]) ).
cnf(t20985,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)],[t9219,t256]) ).
cnf(t20986,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t20985,t9203]) ).
cnf(t20987,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t20986,t256]) ).
cnf(t18581,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t20987]) ).
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(t167,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t332,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t167]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/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(t127,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)],[t127]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox2/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(t128,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)],[t128]) ).
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(t156,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)],[t156]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/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(t129,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)],[t129]) ).
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(t130,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)],[t130]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/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(c117,plain,
coll(sk25,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk25,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h9,plain,
coll(sk25,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi117]) ).
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(h38,plain,
coll(sk20,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h9,h9]) ).
cnf(c119,plain,
coll(sk26,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
coll(sk26,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h14,plain,
coll(sk26,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi119]) ).
cnf(h49,plain,
coll(sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h14,h14]) ).
cnf(h138,plain,
coll(sk26,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h49,h38]) ).
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(c114,plain,
para(sk21,sk22,sk24,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
para(sk21,sk22,sk24,sk20) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h1,plain,
eqangle(sk21,sk22,V0,V1,sk24,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi114]) ).
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/sandbox2/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(h17,plain,
eqangle(sk21,sk22,sk24,sk20,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h1]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X4,X5,X6,X7,X0,X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h59,plain,
eqangle(V0,V1,V0,V1,sk21,sk22,sk24,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi19,h17]) ).
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(eqangle(X4,X5,X6,X7,X8,X9,X10,X11),true,eqangle(X0,X1,X2,X3,X8,X9,X10,X11),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h180,plain,
eqangle(V0,V1,V0,V1,V2,V3,V2,V3) = true,
inference(hyper_resolution,[status(thm)],[hi21,h59,h17]) ).
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(t18,plain,
cyclic(sk20,sk20,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi42,h180,h138]) ).
cnf(t2577,plain,
cyclic(sk20,sk20,sk26,sk25) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t2578,plain,
true = ifeq(true,true,cyclic(sk20,sk26,sk20,sk25),true),
inference(cp,[status(thm)],[t346,t2577]) ).
cnf(t19461,plain,
true = cyclic(sk20,sk26,sk20,sk25),
inference(step,[status(thm)],[t2578,t256]) ).
cnf(t4130,plain,
cyclic(sk20,sk26,sk20,sk25) = true,
inference(orient,[status(thm)],[t19461]) ).
cnf(t4131,plain,
true = ifeq(true,true,cyclic(sk20,sk26,sk25,sk20),true),
inference(cp,[status(thm)],[t348,t4130]) ).
cnf(t19485,plain,
true = cyclic(sk20,sk26,sk25,sk20),
inference(step,[status(thm)],[t4131,t256]) ).
cnf(t4625,plain,
cyclic(sk20,sk26,sk25,sk20) = true,
inference(orient,[status(thm)],[t19485]) ).
cnf(t4628,plain,
true = ifeq(true,true,eqangle(sk25,sk20,sk25,sk26,sk20,sk20,sk20,sk26),true),
inference(cp,[status(thm)],[t343,t4625]) ).
cnf(t19769,plain,
true = eqangle(sk25,sk20,sk25,sk26,sk20,sk20,sk20,sk26),
inference(step,[status(thm)],[t4628,t256]) ).
cnf(t8498,plain,
eqangle(sk25,sk20,sk25,sk26,sk20,sk20,sk20,sk26) = true,
inference(orient,[status(thm)],[t19769]) ).
cnf(t8512,plain,
true = ifeq(cyclic(sk20,sk26,sk25,sk20),true,ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(cyclic(sk20,sk26,sk25,sk20),true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),true),true),
inference(cp,[status(thm)],[t341,t8498]) ).
cnf(t19770,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(cyclic(sk20,sk26,sk25,sk20),true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),true),true),
inference(step,[status(thm)],[t8512,t4625]) ).
cnf(t19771,plain,
true = ifeq(cyclic(sk20,sk26,sk25,sk26),true,ifeq(cyclic(sk20,sk26,sk25,sk20),true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),true),
inference(step,[status(thm)],[t19770,t256]) ).
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(t131,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)],[t131]) ).
cnf(h137,plain,
coll(sk25,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h38,h49]) ).
cnf(h599,plain,
coll(sk25,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h137]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/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(h1806,plain,
coll(sk20,sk25,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi1,h599]) ).
cnf(t27,plain,
cyclic(sk26,sk26,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi42,h180,h1806]) ).
cnf(t2774,plain,
cyclic(sk26,sk26,sk20,sk25) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t2777,plain,
true = ifeq(true,true,cyclic(sk26,sk20,sk26,sk25),true),
inference(cp,[status(thm)],[t346,t2774]) ).
cnf(t19470,plain,
true = cyclic(sk26,sk20,sk26,sk25),
inference(step,[status(thm)],[t2777,t256]) ).
cnf(t4287,plain,
cyclic(sk26,sk20,sk26,sk25) = true,
inference(orient,[status(thm)],[t19470]) ).
cnf(t4288,plain,
true = ifeq(true,true,cyclic(sk26,sk20,sk25,sk26),true),
inference(cp,[status(thm)],[t348,t4287]) ).
cnf(t19491,plain,
true = cyclic(sk26,sk20,sk25,sk26),
inference(step,[status(thm)],[t4288,t256]) ).
cnf(t4729,plain,
cyclic(sk26,sk20,sk25,sk26) = true,
inference(orient,[status(thm)],[t19491]) ).
cnf(t4732,plain,
true = ifeq(true,true,cyclic(sk20,sk26,sk25,sk26),true),
inference(cp,[status(thm)],[t344,t4729]) ).
cnf(t19502,plain,
true = cyclic(sk20,sk26,sk25,sk26),
inference(step,[status(thm)],[t4732,t256]) ).
cnf(t4945,plain,
cyclic(sk20,sk26,sk25,sk26) = true,
inference(orient,[status(thm)],[t19502]) ).
cnf(t19772,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk26,sk25,sk20),true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),true),
inference(step,[status(thm)],[t19771,t4945]) ).
cnf(t19773,plain,
true = ifeq(cyclic(sk20,sk26,sk25,sk20),true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),
inference(step,[status(thm)],[t19772,t256]) ).
cnf(t19774,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),true),
inference(step,[status(thm)],[t19773,t4625]) ).
cnf(t19775,plain,
true = ifeq(true,true,cong(sk20,sk26,sk20,sk26),true),
inference(step,[status(thm)],[t19774,t256]) ).
cnf(t19776,plain,
true = cong(sk20,sk26,sk20,sk26),
inference(step,[status(thm)],[t19775,t256]) ).
cnf(t8513,plain,
cong(sk20,sk26,sk20,sk26) = true,
inference(orient,[status(thm)],[t19776]) ).
cnf(t8516,plain,
true = ifeq(true,true,cong(sk20,sk26,sk26,sk20),true),
inference(cp,[status(thm)],[t323,t8513]) ).
cnf(t19780,plain,
true = cong(sk20,sk26,sk26,sk20),
inference(step,[status(thm)],[t8516,t256]) ).
cnf(t8581,plain,
cong(sk20,sk26,sk26,sk20) = true,
inference(orient,[status(thm)],[t19780]) ).
cnf(t8583,plain,
true = ifeq(true,true,cong(sk26,sk20,sk20,sk26),true),
inference(cp,[status(thm)],[t321,t8581]) ).
cnf(t19781,plain,
true = cong(sk26,sk20,sk20,sk26),
inference(step,[status(thm)],[t8583,t256]) ).
cnf(t8591,plain,
cong(sk26,sk20,sk20,sk26) = true,
inference(orient,[status(thm)],[t19781]) ).
cnf(t8593,plain,
true = ifeq(true,true,cong(sk26,sk20,sk26,sk20),true),
inference(cp,[status(thm)],[t323,t8591]) ).
cnf(t19782,plain,
true = cong(sk26,sk20,sk26,sk20),
inference(step,[status(thm)],[t8593,t256]) ).
cnf(t8600,plain,
cong(sk26,sk20,sk26,sk20) = true,
inference(orient,[status(thm)],[t19782]) ).
cnf(t8609,plain,
true = ifeq(true,true,ifeq(coll(sk26,sk20,sk20),true,midp(sk26,sk20,sk20),true),true),
inference(cp,[status(thm)],[t332,t8600]) ).
cnf(t19783,plain,
true = ifeq(coll(sk26,sk20,sk20),true,midp(sk26,sk20,sk20),true),
inference(step,[status(thm)],[t8609,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(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]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t208,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t299,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t208]) ).
cnf(h54,plain,
para(sk20,sk23,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi8,h15,h0]) ).
cnf(hi66,axiom,
ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h149,plain,
coll(sk20,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi66,h54]) ).
cnf(h627,plain,
coll(sk23,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h149,h149]) ).
cnf(h2068,plain,
coll(sk20,sk20,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h627,h627]) ).
cnf(h5014,plain,
coll(sk26,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h49,h2068]) ).
cnf(t17,plain,
cyclic(sk20,sk20,sk26,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h180,h5014]) ).
cnf(t2560,plain,
cyclic(sk20,sk20,sk26,sk23) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t2563,plain,
true = ifeq(true,true,eqangle(sk26,sk20,sk26,sk20,sk23,sk20,sk23,sk20),true),
inference(cp,[status(thm)],[t343,t2560]) ).
cnf(t19603,plain,
true = eqangle(sk26,sk20,sk26,sk20,sk23,sk20,sk23,sk20),
inference(step,[status(thm)],[t2563,t256]) ).
cnf(t6474,plain,
eqangle(sk26,sk20,sk26,sk20,sk23,sk20,sk23,sk20) = true,
inference(orient,[status(thm)],[t19603]) ).
cnf(t6484,plain,
true = ifeq(true,true,ifeq(para(sk23,sk20,sk23,sk20),true,para(sk26,sk20,sk26,sk20),true),true),
inference(cp,[status(thm)],[t299,t6474]) ).
cnf(t19604,plain,
true = ifeq(para(sk23,sk20,sk23,sk20),true,para(sk26,sk20,sk26,sk20),true),
inference(step,[status(thm)],[t6484,t256]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox2/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(h16,plain,
perp(sk11(sk20,sk21,sk22,sk23),sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi6,h0]) ).
cnf(h57,plain,
perp(sk23,sk20,sk11(sk20,sk21,sk22,sk23),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h16]) ).
cnf(t34,plain,
para(sk23,sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h57,h16]) ).
cnf(t1881,plain,
para(sk23,sk20,sk23,sk20) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t19605,plain,
true = ifeq(true,true,para(sk26,sk20,sk26,sk20),true),
inference(step,[status(thm)],[t19604,t1881]) ).
cnf(t19606,plain,
true = para(sk26,sk20,sk26,sk20),
inference(step,[status(thm)],[t19605,t256]) ).
cnf(t6488,plain,
para(sk26,sk20,sk26,sk20) = true,
inference(orient,[status(thm)],[t19606]) ).
cnf(t6490,plain,
true = ifeq(true,true,coll(sk26,sk20,sk20),true),
inference(cp,[status(thm)],[t295,t6488]) ).
cnf(t19607,plain,
true = coll(sk26,sk20,sk20),
inference(step,[status(thm)],[t6490,t256]) ).
cnf(t6515,plain,
coll(sk26,sk20,sk20) = true,
inference(orient,[status(thm)],[t19607]) ).
cnf(t19784,plain,
true = ifeq(true,true,midp(sk26,sk20,sk20),true),
inference(step,[status(thm)],[t19783,t6515]) ).
cnf(t19785,plain,
true = midp(sk26,sk20,sk20),
inference(step,[status(thm)],[t19784,t256]) ).
cnf(t8639,plain,
midp(sk26,sk20,sk20) = true,
inference(orient,[status(thm)],[t19785]) ).
cnf(t18582,plain,
true = ifeq(true,true,midp(sk26,X1,X1),true),
inference(cp,[status(thm)],[t18581,t8639]) ).
cnf(t20988,plain,
true = midp(sk26,X1,X1),
inference(step,[status(thm)],[t18582,t256]) ).
cnf(t18590,plain,
midp(sk26,X1,X1) = true,
inference(orient,[status(thm)],[t20988]) ).
cnf(t18591,plain,
true = ifeq(true,true,cong(sk26,X1,sk26,X1),true),
inference(cp,[status(thm)],[t363,t18590]) ).
cnf(t20993,plain,
true = cong(sk26,X1,sk26,X1),
inference(step,[status(thm)],[t18591,t256]) ).
cnf(t18671,plain,
cong(sk26,X1,sk26,X1) = true,
inference(orient,[status(thm)],[t20993]) ).
cnf(t18682,plain,
true = ifeq(true,true,ifeq(cong(sk26,X1,sk26,X1),true,perp(sk26,sk26,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t18671]) ).
cnf(t20998,plain,
true = ifeq(cong(sk26,X1,sk26,X1),true,perp(sk26,sk26,X2,X1),true),
inference(step,[status(thm)],[t18682,t256]) ).
cnf(t20999,plain,
true = ifeq(true,true,perp(sk26,sk26,X2,X1),true),
inference(step,[status(thm)],[t20998,t18671]) ).
cnf(t21000,plain,
true = perp(sk26,sk26,X2,X1),
inference(step,[status(thm)],[t20999,t256]) ).
cnf(t18819,plain,
perp(sk26,sk26,X1,X2) = true,
inference(orient,[status(thm)],[t21000]) ).
cnf(t18823,plain,
true = ifeq(true,true,perp(X1,X2,sk26,sk26),true),
inference(cp,[status(thm)],[t269,t18819]) ).
cnf(t21016,plain,
true = perp(X1,X2,sk26,sk26),
inference(step,[status(thm)],[t18823,t256]) ).
cnf(t19064,plain,
perp(X1,X2,sk26,sk26) = true,
inference(orient,[status(thm)],[t21016]) ).
cnf(t19068,plain,
true = ifeq(true,true,ifeq(perp(sk26,sk26,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t260,t19064]) ).
cnf(t21033,plain,
true = ifeq(perp(sk26,sk26,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t19068,t256]) ).
cnf(t21034,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t21033,t18819]) ).
cnf(t21035,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t21034,t256]) ).
cnf(t19402,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t21035]) ).
cnf(c120,plain,
~ para(sk25,sk26,sk20,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk25,sk26,sk20,sk23) != true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t19402]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO609+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 12:37:28 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 115.46/16.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 115.46/16.92 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------