%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO642+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 : n011.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 01:18:22 PM UTC 2026
% Result : Theorem 101.04s 28.16s
% Output : Proof 101.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 87
% Number of leaves : 22
% Syntax : Number of formulae : 249 ( 165 unt; 0 def)
% Number of atoms : 417 ( 162 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 261 ( 93 ~; 87 |; 59 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 19 ( 19 usr; 18 con; 0-4 aty)
% Number of variables : 865 ( 127 sgn 322 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
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(t140,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t271,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t140]) ).
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(t73,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t268,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t73]) ).
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(t74,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t266,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t74]) ).
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(t71,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t336,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t71]) ).
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(t216,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t333,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t216]) ).
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(t153,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t285,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t153]) ).
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(t81,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t292,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t81]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t198,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t305,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t198]) ).
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(t143,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t312,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t143]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD63) ).
fof(f63_nnf,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [M,A,B,C,D] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( para(X0,X2,X1,X3)
| ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi63,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X0,X3,X4),true,para(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
fof(f94,conjecture,
! [A,B,O,C,P,D,G,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ( coll(F,C,P)
& coll(F,A,D)
& coll(E,B,P)
& coll(E,A,C)
& coll(G,A,D)
& coll(G,B,P)
& circle(C,B,D,NWPNT8)
& circle(O,A,D,NWPNT7)
& circle(C,B,NWPNT5,NWPNT6)
& circle(O,A,P,NWPNT4)
& circle(O,A,C,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,B,A) )
=> perp(E,F,A,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL81109108) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,O,C,P,D,G,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ( coll(F,C,P)
& coll(F,A,D)
& coll(E,B,P)
& coll(E,A,C)
& coll(G,A,D)
& coll(G,B,P)
& circle(C,B,D,NWPNT8)
& circle(O,A,D,NWPNT7)
& circle(C,B,NWPNT5,NWPNT6)
& circle(O,A,P,NWPNT4)
& circle(O,A,C,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,B,A) )
=> perp(E,F,A,D) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,O,C,P,D,G,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ~ perp(E,F,A,D)
& coll(F,C,P)
& coll(F,A,D)
& coll(E,B,P)
& coll(E,A,C)
& coll(G,A,D)
& coll(G,B,P)
& circle(C,B,D,NWPNT8)
& circle(O,A,D,NWPNT7)
& circle(C,B,NWPNT5,NWPNT6)
& circle(O,A,P,NWPNT4)
& circle(O,A,C,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,B,A) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk27,sk28,sk20,sk25)
& coll(sk28,sk23,sk24)
& coll(sk28,sk20,sk25)
& coll(sk27,sk21,sk24)
& coll(sk27,sk20,sk23)
& coll(sk26,sk20,sk25)
& coll(sk26,sk21,sk24)
& circle(sk23,sk21,sk25,sk36)
& circle(sk22,sk20,sk25,sk35)
& circle(sk23,sk21,sk33,sk34)
& circle(sk22,sk20,sk24,sk32)
& circle(sk22,sk20,sk23,sk31)
& circle(sk22,sk20,sk29,sk30)
& midp(sk22,sk21,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31,sk32,sk33,sk34,sk35,sk36])],[f94_nnf]) ).
cnf(c113,plain,
midp(sk22,sk21,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
midp(sk22,sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h6,plain,
para(sk21,sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi63,hi113,hi113]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h89,plain,
eqangle(sk21,sk21,V0,V1,sk20,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h6]) ).
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(hi18,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X2,X3,X0,X1,X6,X7,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t35,plain,
eqangle(X1,X2,sk21,sk21,X1,X2,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi18,h89]) ).
cnf(t1821,plain,
eqangle(X1,X2,sk21,sk21,X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t1822,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk21,sk21,sk20,sk20),true),
inference(cp,[status(thm)],[t312,t1821]) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t32]) ).
cnf(t15336,plain,
true = eqangle(X1,X2,X1,X2,sk21,sk21,sk20,sk20),
inference(step,[status(thm)],[t1822,t256]) ).
cnf(t5287,plain,
eqangle(X1,X2,X1,X2,sk21,sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t15336]) ).
cnf(t5292,plain,
true = ifeq(true,true,ifeq(para(sk21,sk21,sk20,sk20),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t305,t5287]) ).
cnf(t15337,plain,
true = ifeq(para(sk21,sk21,sk20,sk20),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t5292,t256]) ).
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(t114,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t314,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t114]) ).
cnf(t40,plain,
eqangle(sk21,sk21,X1,X2,sk20,sk20,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h6]) ).
cnf(t1949,plain,
eqangle(sk21,sk21,X1,X2,sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(t1951,plain,
true = ifeq(true,true,para(sk21,sk21,sk20,sk20),true),
inference(cp,[status(thm)],[t314,t1949]) ).
cnf(t15306,plain,
true = para(sk21,sk21,sk20,sk20),
inference(step,[status(thm)],[t1951,t256]) ).
cnf(t4629,plain,
para(sk21,sk21,sk20,sk20) = true,
inference(orient,[status(thm)],[t15306]) ).
cnf(t15338,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t15337,t4629]) ).
cnf(t15339,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t15338,t256]) ).
cnf(t5297,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t15339]) ).
cnf(t5317,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),true),
inference(cp,[status(thm)],[t333,t5297]) ).
cnf(t16117,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)],[t5317,t256]) ).
cnf(t16118,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t16117,t5297]) ).
cnf(t16119,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t16118,t256]) ).
cnf(t11842,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t16119]) ).
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(t131,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t272,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t131]) ).
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(t119,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t260,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t119]) ).
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(t65,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t263,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t65]) ).
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(t66,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t261,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t66]) ).
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(t72,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t353,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t72]) ).
cnf(t5298,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t353,t5297]) ).
cnf(t15340,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t5298,t256]) ).
cnf(t5326,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t15340]) ).
cnf(t5328,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t5326]) ).
cnf(t15341,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t5328,t256]) ).
cnf(t5371,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t15341]) ).
cnf(t5374,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t5371]) ).
cnf(t15342,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t5374,t256]) ).
cnf(t5403,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t15342]) ).
cnf(t5406,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t5403]) ).
cnf(t15343,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t5406,t256]) ).
cnf(t15344,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t15343,t5403]) ).
cnf(t15345,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t15344,t256]) ).
cnf(t5438,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t15345]) ).
cnf(t15356,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t272,t5438]) ).
cnf(t15357,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t15356,t256]) ).
cnf(t5445,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t15357]) ).
cnf(t12732,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t5445]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t141,plain,
ifeq(cong(X1,X2,X3,X4),true,ifeq(cong(X3,X4,X5,X6),true,cong(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t265,plain,
ifeq(cong(X1,X2,X3,X4),true,ifeq(cong(X3,X4,X5,X6),true,cong(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t141]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t24,plain,
midp(sk22,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi113]) ).
cnf(t1987,plain,
midp(sk22,sk20,sk21) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(t1990,plain,
true = ifeq(true,true,cong(sk22,sk20,sk22,sk21),true),
inference(cp,[status(thm)],[t336,t1987]) ).
cnf(t15307,plain,
true = cong(sk22,sk20,sk22,sk21),
inference(step,[status(thm)],[t1990,t256]) ).
cnf(t4652,plain,
cong(sk22,sk20,sk22,sk21) = true,
inference(orient,[status(thm)],[t15307]) ).
cnf(t4666,plain,
true = ifeq(true,true,ifeq(cong(sk22,sk21,X1,X2),true,cong(sk22,sk20,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t4652]) ).
cnf(t16287,plain,
true = ifeq(cong(sk22,sk21,X1,X2),true,cong(sk22,sk20,X1,X2),true),
inference(step,[status(thm)],[t4666,t256]) ).
cnf(t13784,plain,
ifeq(cong(sk22,sk21,X1,X2),true,cong(sk22,sk20,X1,X2),true) = true,
inference(orient,[status(thm)],[t16287]) ).
cnf(t25,plain,
midp(sk22,sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t2019,plain,
midp(sk22,sk21,sk20) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t2020,plain,
true = ifeq(true,true,cong(sk22,sk21,sk22,sk20),true),
inference(cp,[status(thm)],[t336,t2019]) ).
cnf(t15308,plain,
true = cong(sk22,sk21,sk22,sk20),
inference(step,[status(thm)],[t2020,t256]) ).
cnf(t4690,plain,
cong(sk22,sk21,sk22,sk20) = true,
inference(orient,[status(thm)],[t15308]) ).
cnf(t13787,plain,
true = ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),
inference(cp,[status(thm)],[t13784,t4690]) ).
cnf(t16289,plain,
true = cong(sk22,sk20,sk22,sk20),
inference(step,[status(thm)],[t13787,t256]) ).
cnf(t13805,plain,
cong(sk22,sk20,sk22,sk20) = true,
inference(orient,[status(thm)],[t16289]) ).
cnf(t13808,plain,
true = ifeq(true,true,midp(sk22,sk20,sk20),true),
inference(cp,[status(thm)],[t12732,t13805]) ).
cnf(t16290,plain,
true = midp(sk22,sk20,sk20),
inference(step,[status(thm)],[t13808,t256]) ).
cnf(t13838,plain,
midp(sk22,sk20,sk20) = true,
inference(orient,[status(thm)],[t16290]) ).
cnf(t13845,plain,
true = ifeq(true,true,midp(sk22,X1,X1),true),
inference(cp,[status(thm)],[t11842,t13838]) ).
cnf(t16291,plain,
true = midp(sk22,X1,X1),
inference(step,[status(thm)],[t13845,t256]) ).
cnf(t13864,plain,
midp(sk22,X1,X1) = true,
inference(orient,[status(thm)],[t16291]) ).
cnf(t13873,plain,
true = ifeq(true,true,cong(sk22,X1,sk22,X1),true),
inference(cp,[status(thm)],[t336,t13864]) ).
cnf(t16301,plain,
true = cong(sk22,X1,sk22,X1),
inference(step,[status(thm)],[t13873,t256]) ).
cnf(t14010,plain,
cong(sk22,X1,sk22,X1) = true,
inference(orient,[status(thm)],[t16301]) ).
cnf(t14021,plain,
true = ifeq(true,true,ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t14010]) ).
cnf(t16313,plain,
true = ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t14021,t256]) ).
cnf(t16314,plain,
true = ifeq(true,true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t16313,t14010]) ).
cnf(t16315,plain,
true = perp(sk22,sk22,X2,X1),
inference(step,[status(thm)],[t16314,t256]) ).
cnf(t14229,plain,
perp(sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t16315]) ).
cnf(t14231,plain,
true = ifeq(true,true,perp(X1,X2,sk22,sk22),true),
inference(cp,[status(thm)],[t292,t14229]) ).
cnf(t16328,plain,
true = perp(X1,X2,sk22,sk22),
inference(step,[status(thm)],[t14231,t256]) ).
cnf(t14389,plain,
perp(X1,X2,sk22,sk22) = true,
inference(orient,[status(thm)],[t16328]) ).
cnf(t14396,plain,
true = ifeq(true,true,ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t14389]) ).
cnf(t16341,plain,
true = ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t14396,t256]) ).
cnf(t16342,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t16341,t14229]) ).
cnf(t16343,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t16342,t256]) ).
cnf(t14616,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t16343]) ).
cnf(t16355,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)],[t333,t14616]) ).
cnf(t16356,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)],[t16355,t256]) ).
cnf(t16357,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t16356,t14616]) ).
cnf(t16358,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t16357,t256]) ).
cnf(t14623,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t16358]) ).
cnf(t15122,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t14623]) ).
cnf(t14013,plain,
true = ifeq(true,true,cong(sk22,X1,X1,sk22),true),
inference(cp,[status(thm)],[t268,t14010]) ).
cnf(t16311,plain,
true = cong(sk22,X1,X1,sk22),
inference(step,[status(thm)],[t14013,t256]) ).
cnf(t14197,plain,
cong(sk22,X1,X1,sk22) = true,
inference(orient,[status(thm)],[t16311]) ).
cnf(t14199,plain,
true = ifeq(true,true,cong(X1,sk22,sk22,X1),true),
inference(cp,[status(thm)],[t266,t14197]) ).
cnf(t16325,plain,
true = cong(X1,sk22,sk22,X1),
inference(step,[status(thm)],[t14199,t256]) ).
cnf(t14347,plain,
cong(X1,sk22,sk22,X1) = true,
inference(orient,[status(thm)],[t16325]) ).
cnf(t14349,plain,
true = ifeq(true,true,cong(X1,sk22,X1,sk22),true),
inference(cp,[status(thm)],[t268,t14347]) ).
cnf(t16337,plain,
true = cong(X1,sk22,X1,sk22),
inference(step,[status(thm)],[t14349,t256]) ).
cnf(t14520,plain,
cong(X1,sk22,X1,sk22) = true,
inference(orient,[status(thm)],[t16337]) ).
cnf(t14521,plain,
true = ifeq(true,true,midp(X1,sk22,sk22),true),
inference(cp,[status(thm)],[t12732,t14520]) ).
cnf(t16338,plain,
true = midp(X1,sk22,sk22),
inference(step,[status(thm)],[t14521,t256]) ).
cnf(t14550,plain,
midp(X1,sk22,sk22) = true,
inference(orient,[status(thm)],[t16338]) ).
cnf(t14551,plain,
true = ifeq(true,true,midp(X1,X2,X2),true),
inference(cp,[status(thm)],[t11842,t14550]) ).
cnf(t16339,plain,
true = midp(X1,X2,X2),
inference(step,[status(thm)],[t14551,t256]) ).
cnf(t14569,plain,
midp(X1,X2,X2) = true,
inference(orient,[status(thm)],[t16339]) ).
cnf(t15123,plain,
true = ifeq(true,true,midp(X1,X2,X3),true),
inference(cp,[status(thm)],[t15122,t14569]) ).
cnf(t16414,plain,
true = midp(X1,X2,X3),
inference(step,[status(thm)],[t15123,t256]) ).
cnf(t15136,plain,
midp(X1,X2,X3) = true,
inference(orient,[status(thm)],[t16414]) ).
cnf(t16415,plain,
ifeq(true,true,cong(X1,X2,X1,X3),true) = true,
inference(step,[status(thm)],[t336,t15136]) ).
cnf(t16416,plain,
cong(X1,X2,X1,X3) = true,
inference(step,[status(thm)],[t16415,t256]) ).
cnf(t15137,plain,
cong(X1,X2,X1,X3) = true,
inference(rw,[status(thm)],[t16416]) ).
cnf(t15143,plain,
cong(X1,X2,X1,X3) = true,
inference(orient,[status(thm)],[t15137]) ).
cnf(t15145,plain,
true = ifeq(true,true,cong(X1,X2,X3,X1),true),
inference(cp,[status(thm)],[t268,t15143]) ).
cnf(t16458,plain,
true = cong(X1,X2,X3,X1),
inference(step,[status(thm)],[t15145,t256]) ).
cnf(t15167,plain,
cong(X1,X2,X3,X1) = true,
inference(orient,[status(thm)],[t16458]) ).
cnf(t15169,plain,
true = ifeq(true,true,cong(X1,X2,X2,X3),true),
inference(cp,[status(thm)],[t266,t15167]) ).
cnf(t16463,plain,
true = cong(X1,X2,X2,X3),
inference(step,[status(thm)],[t15169,t256]) ).
cnf(t15191,plain,
cong(X1,X2,X2,X3) = true,
inference(orient,[status(thm)],[t16463]) ).
cnf(t15195,plain,
true = ifeq(true,true,cong(X1,X2,X3,X2),true),
inference(cp,[status(thm)],[t268,t15191]) ).
cnf(t16465,plain,
true = cong(X1,X2,X3,X2),
inference(step,[status(thm)],[t15195,t256]) ).
cnf(t15223,plain,
cong(X1,X2,X3,X2) = true,
inference(orient,[status(thm)],[t16465]) ).
cnf(t16466,plain,
ifeq(true,true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(step,[status(thm)],[t271,t15223]) ).
cnf(t16467,plain,
ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true) = true,
inference(step,[status(thm)],[t16466,t256]) ).
cnf(t16468,plain,
ifeq(true,true,perp(X1,X3,X2,X4),true) = true,
inference(step,[status(thm)],[t16467,t15223]) ).
cnf(t16469,plain,
perp(X1,X3,X2,X4) = true,
inference(step,[status(thm)],[t16468,t256]) ).
cnf(t15235,plain,
perp(X1,X3,X2,X4) = true,
inference(rw,[status(thm)],[t16469]) ).
cnf(t15260,plain,
perp(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t15235]) ).
cnf(c126,plain,
~ perp(sk27,sk28,sk20,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk27,sk28,sk20,sk25) != true,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t15260]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO642+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/15.28 % CPULimit : 300
% 0.06/15.28 % WCLimit : 300
% 0.06/15.28 % DateTime : Wed Sep 23 12:41:10 UTC 2026
% 0.06/15.28 % CPUTime :
% 0.06/15.28 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 101.04/28.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 101.04/28.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------