%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO587+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 : n026.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 01:18:13 PM UTC 2026
% Result : Theorem 136.07s 17.87s
% Output : Proof 136.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 25
% Syntax : Number of formulae : 283 ( 187 unt; 0 def)
% Number of atoms : 455 ( 183 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 286 ( 114 ~; 108 |; 39 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-4 aty)
% Number of variables : 880 ( 110 sgn 348 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,conjecture,
! [A,C,B,D,P,Q,R,S,O] :
( ( coll(O,Q,S)
& coll(O,P,R)
& midp(S,A,D)
& midp(R,D,C)
& midp(Q,C,B)
& midp(P,B,A)
& perp(A,C,B,D) )
=> cong(O,S,O,R) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416049) ).
fof(f94_neg,negated_conjecture,
~ ! [A,C,B,D,P,Q,R,S,O] :
( ( coll(O,Q,S)
& coll(O,P,R)
& midp(S,A,D)
& midp(R,D,C)
& midp(Q,C,B)
& midp(P,B,A)
& perp(A,C,B,D) )
=> cong(O,S,O,R) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,C,B,D,P,Q,R,S,O] :
( ~ cong(O,S,O,R)
& coll(O,Q,S)
& coll(O,P,R)
& midp(S,A,D)
& midp(R,D,C)
& midp(Q,C,B)
& midp(P,B,A)
& perp(A,C,B,D) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cong(sk28,sk27,sk28,sk26)
& coll(sk28,sk25,sk27)
& coll(sk28,sk24,sk26)
& midp(sk27,sk20,sk23)
& midp(sk26,sk23,sk21)
& midp(sk25,sk21,sk22)
& midp(sk24,sk22,sk20)
& perp(sk20,sk21,sk22,sk23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28])],[f94_nnf]) ).
cnf(c120,plain,
~ cong(sk28,sk27,sk28,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t36,plain,
cong(sk28,sk27,sk28,sk26) = false,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(t3533,plain,
cong(sk28,sk27,sk28,sk26) = false,
inference(orient,[status(thm)],[t36]) ).
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(t118,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)],[t118]) ).
cnf(t3535,plain,
true = ifeq(midp(sk28,sk27,sk26),true,false,true),
inference(cp,[status(thm)],[t336,t3533]) ).
cnf(t6292,plain,
ifeq(midp(sk28,sk27,sk26),true,false,true) = true,
inference(orient,[status(thm)],[t3535]) ).
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(t226,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)],[t226]) ).
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t189,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(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)],[t189]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t128,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)],[t128]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t176,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(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)],[t176]) ).
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(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(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)],[t208]) ).
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/sandbox/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(t182,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t306,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t182]) ).
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(t179,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)],[t179]) ).
fof(f44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD44) ).
fof(f44_nnf,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [E,A,B,F,C] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( para(X3,X4,X1,X2)
| ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi44,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X3,X1,X4),true,para(X0,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(c116,plain,
midp(sk26,sk23,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
midp(sk26,sk23,sk21) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h51,plain,
para(sk26,sk26,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi44,hi116,hi116]) ).
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(t56,plain,
eqangle(sk26,sk26,X1,X2,sk21,sk21,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h51]) ).
cnf(t1872,plain,
eqangle(sk26,sk26,X1,X2,sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t56]) ).
cnf(t1875,plain,
true = ifeq(true,true,eqangle(sk26,sk26,sk21,sk21,X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t312,t1872]) ).
cnf(t46,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t46]) ).
cnf(t25781,plain,
true = eqangle(sk26,sk26,sk21,sk21,X1,X2,X1,X2),
inference(step,[status(thm)],[t1875,t256]) ).
cnf(t6398,plain,
eqangle(sk26,sk26,sk21,sk21,X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t25781]) ).
cnf(t6401,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk26,sk26,sk21,sk21),true),
inference(cp,[status(thm)],[t306,t6398]) ).
cnf(t25977,plain,
true = eqangle(X1,X2,X1,X2,sk26,sk26,sk21,sk21),
inference(step,[status(thm)],[t6401,t256]) ).
cnf(t9431,plain,
eqangle(X1,X2,X1,X2,sk26,sk26,sk21,sk21) = true,
inference(orient,[status(thm)],[t25977]) ).
cnf(t9436,plain,
true = ifeq(true,true,ifeq(para(sk26,sk26,sk21,sk21),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t305,t9431]) ).
cnf(t25978,plain,
true = ifeq(para(sk26,sk26,sk21,sk21),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t9436,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(t161,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)],[t161]) ).
cnf(t1874,plain,
true = ifeq(true,true,para(sk26,sk26,sk21,sk21),true),
inference(cp,[status(thm)],[t314,t1872]) ).
cnf(t25711,plain,
true = para(sk26,sk26,sk21,sk21),
inference(step,[status(thm)],[t1874,t256]) ).
cnf(t5010,plain,
para(sk26,sk26,sk21,sk21) = true,
inference(orient,[status(thm)],[t25711]) ).
cnf(t25979,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t25978,t5010]) ).
cnf(t25980,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t25979,t256]) ).
cnf(t9441,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t25980]) ).
cnf(t9458,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,t9441]) ).
cnf(t27209,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)],[t9458,t256]) ).
cnf(t27210,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t27209,t9441]) ).
cnf(t27211,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t27210,t256]) ).
cnf(t20763,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t27211]) ).
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(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(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)],[t167]) ).
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(t357,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(t160,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(t359,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t160]) ).
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(t123,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t362,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t123]) ).
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(t124,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t360,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t124]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(c117,plain,
midp(sk27,sk20,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
midp(sk27,sk20,sk23) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h82,plain,
cong(sk27,sk20,sk27,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi117]) ).
fof(f12,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD13) ).
fof(f12_nnf,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [O,A,B,C,D] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( cyclic(X0,X1,X2,X3)
| ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(cong(X0,X1,X0,X3),true,ifeq(cong(X0,X1,X0,X4),true,cyclic(X1,X2,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t40,plain,
cyclic(sk20,sk23,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi12,h82,h82,h82]) ).
cnf(t3107,plain,
cyclic(sk20,sk23,sk23,sk23) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(t3108,plain,
true = ifeq(true,true,cyclic(sk23,sk20,sk23,sk23),true),
inference(cp,[status(thm)],[t360,t3107]) ).
cnf(t25722,plain,
true = cyclic(sk23,sk20,sk23,sk23),
inference(step,[status(thm)],[t3108,t256]) ).
cnf(t5322,plain,
cyclic(sk23,sk20,sk23,sk23) = true,
inference(orient,[status(thm)],[t25722]) ).
cnf(t5323,plain,
true = ifeq(true,true,cyclic(sk23,sk23,sk20,sk23),true),
inference(cp,[status(thm)],[t362,t5322]) ).
cnf(t25747,plain,
true = cyclic(sk23,sk23,sk20,sk23),
inference(step,[status(thm)],[t5323,t256]) ).
cnf(t5853,plain,
cyclic(sk23,sk23,sk20,sk23) = true,
inference(orient,[status(thm)],[t25747]) ).
cnf(t5856,plain,
true = ifeq(true,true,eqangle(sk20,sk23,sk20,sk23,sk23,sk23,sk23,sk23),true),
inference(cp,[status(thm)],[t359,t5853]) ).
cnf(t25943,plain,
true = eqangle(sk20,sk23,sk20,sk23,sk23,sk23,sk23,sk23),
inference(step,[status(thm)],[t5856,t256]) ).
cnf(t9102,plain,
eqangle(sk20,sk23,sk20,sk23,sk23,sk23,sk23,sk23) = true,
inference(orient,[status(thm)],[t25943]) ).
cnf(t9115,plain,
true = ifeq(cyclic(sk23,sk23,sk20,sk23),true,ifeq(cyclic(sk23,sk23,sk20,sk23),true,ifeq(cyclic(sk23,sk23,sk20,sk23),true,ifeq(true,true,cong(sk23,sk23,sk23,sk23),true),true),true),true),
inference(cp,[status(thm)],[t357,t9102]) ).
cnf(t25944,plain,
true = ifeq(true,true,ifeq(cyclic(sk23,sk23,sk20,sk23),true,ifeq(cyclic(sk23,sk23,sk20,sk23),true,ifeq(true,true,cong(sk23,sk23,sk23,sk23),true),true),true),true),
inference(step,[status(thm)],[t9115,t5853]) ).
cnf(t25945,plain,
true = ifeq(cyclic(sk23,sk23,sk20,sk23),true,ifeq(cyclic(sk23,sk23,sk20,sk23),true,ifeq(true,true,cong(sk23,sk23,sk23,sk23),true),true),true),
inference(step,[status(thm)],[t25944,t256]) ).
cnf(t25946,plain,
true = ifeq(true,true,ifeq(cyclic(sk23,sk23,sk20,sk23),true,ifeq(true,true,cong(sk23,sk23,sk23,sk23),true),true),true),
inference(step,[status(thm)],[t25945,t5853]) ).
cnf(t25947,plain,
true = ifeq(cyclic(sk23,sk23,sk20,sk23),true,ifeq(true,true,cong(sk23,sk23,sk23,sk23),true),true),
inference(step,[status(thm)],[t25946,t256]) ).
cnf(t25948,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk23,sk23,sk23,sk23),true),true),
inference(step,[status(thm)],[t25947,t5853]) ).
cnf(t25949,plain,
true = ifeq(true,true,cong(sk23,sk23,sk23,sk23),true),
inference(step,[status(thm)],[t25948,t256]) ).
cnf(t25950,plain,
true = cong(sk23,sk23,sk23,sk23),
inference(step,[status(thm)],[t25949,t256]) ).
cnf(t9116,plain,
cong(sk23,sk23,sk23,sk23) = true,
inference(orient,[status(thm)],[t25950]) ).
cnf(t9126,plain,
true = ifeq(true,true,ifeq(coll(sk23,sk23,sk23),true,midp(sk23,sk23,sk23),true),true),
inference(cp,[status(thm)],[t272,t9116]) ).
cnf(t25951,plain,
true = ifeq(coll(sk23,sk23,sk23),true,midp(sk23,sk23,sk23),true),
inference(step,[status(thm)],[t9126,t256]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(t119,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)],[t119]) ).
cnf(t5325,plain,
true = ifeq(true,true,eqangle(sk23,sk23,sk23,sk20,sk23,sk23,sk23,sk20),true),
inference(cp,[status(thm)],[t359,t5322]) ).
cnf(t25921,plain,
true = eqangle(sk23,sk23,sk23,sk20,sk23,sk23,sk23,sk20),
inference(step,[status(thm)],[t5325,t256]) ).
cnf(t8866,plain,
eqangle(sk23,sk23,sk23,sk20,sk23,sk23,sk23,sk20) = true,
inference(orient,[status(thm)],[t25921]) ).
cnf(t8868,plain,
true = ifeq(true,true,para(sk23,sk23,sk23,sk23),true),
inference(cp,[status(thm)],[t314,t8866]) ).
cnf(t25922,plain,
true = para(sk23,sk23,sk23,sk23),
inference(step,[status(thm)],[t8868,t256]) ).
cnf(t8880,plain,
para(sk23,sk23,sk23,sk23) = true,
inference(orient,[status(thm)],[t25922]) ).
cnf(t8881,plain,
true = ifeq(true,true,coll(sk23,sk23,sk23),true),
inference(cp,[status(thm)],[t353,t8880]) ).
cnf(t25923,plain,
true = coll(sk23,sk23,sk23),
inference(step,[status(thm)],[t8881,t256]) ).
cnf(t8900,plain,
coll(sk23,sk23,sk23) = true,
inference(orient,[status(thm)],[t25923]) ).
cnf(t25952,plain,
true = ifeq(true,true,midp(sk23,sk23,sk23),true),
inference(step,[status(thm)],[t25951,t8900]) ).
cnf(t25953,plain,
true = midp(sk23,sk23,sk23),
inference(step,[status(thm)],[t25952,t256]) ).
cnf(t9154,plain,
midp(sk23,sk23,sk23) = true,
inference(orient,[status(thm)],[t25953]) ).
cnf(t20764,plain,
true = ifeq(true,true,midp(sk23,X1,X1),true),
inference(cp,[status(thm)],[t20763,t9154]) ).
cnf(t27212,plain,
true = midp(sk23,X1,X1),
inference(step,[status(thm)],[t20764,t256]) ).
cnf(t20771,plain,
midp(sk23,X1,X1) = true,
inference(orient,[status(thm)],[t27212]) ).
cnf(t20772,plain,
true = ifeq(true,true,cong(sk23,X1,sk23,X1),true),
inference(cp,[status(thm)],[t336,t20771]) ).
cnf(t27216,plain,
true = cong(sk23,X1,sk23,X1),
inference(step,[status(thm)],[t20772,t256]) ).
cnf(t20851,plain,
cong(sk23,X1,sk23,X1) = true,
inference(orient,[status(thm)],[t27216]) ).
cnf(t20866,plain,
true = ifeq(true,true,ifeq(cong(sk23,X1,sk23,X1),true,perp(sk23,sk23,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t20851]) ).
cnf(t27221,plain,
true = ifeq(cong(sk23,X1,sk23,X1),true,perp(sk23,sk23,X2,X1),true),
inference(step,[status(thm)],[t20866,t256]) ).
cnf(t27222,plain,
true = ifeq(true,true,perp(sk23,sk23,X2,X1),true),
inference(step,[status(thm)],[t27221,t20851]) ).
cnf(t27223,plain,
true = perp(sk23,sk23,X2,X1),
inference(step,[status(thm)],[t27222,t256]) ).
cnf(t21019,plain,
perp(sk23,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t27223]) ).
cnf(t21020,plain,
true = ifeq(true,true,perp(X1,X2,sk23,sk23),true),
inference(cp,[status(thm)],[t292,t21019]) ).
cnf(t27238,plain,
true = perp(X1,X2,sk23,sk23),
inference(step,[status(thm)],[t21020,t256]) ).
cnf(t21237,plain,
perp(X1,X2,sk23,sk23) = true,
inference(orient,[status(thm)],[t27238]) ).
cnf(t21244,plain,
true = ifeq(true,true,ifeq(perp(sk23,sk23,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t21237]) ).
cnf(t27246,plain,
true = ifeq(perp(sk23,sk23,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t21244,t256]) ).
cnf(t27247,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t27246,t21019]) ).
cnf(t27248,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t27247,t256]) ).
cnf(t21448,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t27248]) ).
cnf(t27260,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,t21448]) ).
cnf(t27261,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)],[t27260,t256]) ).
cnf(t27262,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t27261,t21448]) ).
cnf(t27263,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t27262,t256]) ).
cnf(t21455,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t27263]) ).
cnf(t22534,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t21455]) ).
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(t166,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)],[t166]) ).
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(t90,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)],[t90]) ).
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(t91,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)],[t91]) ).
cnf(t9442,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t353,t9441]) ).
cnf(t25981,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t9442,t256]) ).
cnf(t9467,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t25981]) ).
cnf(t9469,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t9467]) ).
cnf(t25982,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t9469,t256]) ).
cnf(t9510,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t25982]) ).
cnf(t9513,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t9510]) ).
cnf(t25983,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t9513,t256]) ).
cnf(t9542,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t25983]) ).
cnf(t9545,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t9542]) ).
cnf(t25984,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t9545,t256]) ).
cnf(t25985,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t25984,t9542]) ).
cnf(t25986,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t25985,t256]) ).
cnf(t9576,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t25986]) ).
cnf(t25997,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t272,t9576]) ).
cnf(t25998,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t25997,t256]) ).
cnf(t9583,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t25998]) ).
cnf(t25549,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t9583]) ).
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(t120,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)],[t120]) ).
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(t121,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)],[t121]) ).
cnf(t23,plain,
midp(sk27,sk20,sk23) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(t2104,plain,
midp(sk27,sk20,sk23) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t22564,plain,
true = ifeq(true,true,midp(sk27,X1,X2),true),
inference(cp,[status(thm)],[t22534,t2104]) ).
cnf(t27392,plain,
true = midp(sk27,X1,X2),
inference(step,[status(thm)],[t22564,t256]) ).
cnf(t22634,plain,
midp(sk27,X1,X2) = true,
inference(orient,[status(thm)],[t27392]) ).
cnf(t22635,plain,
true = ifeq(true,true,cong(sk27,X1,sk27,X2),true),
inference(cp,[status(thm)],[t336,t22634]) ).
cnf(t27404,plain,
true = cong(sk27,X1,sk27,X2),
inference(step,[status(thm)],[t22635,t256]) ).
cnf(t22846,plain,
cong(sk27,X1,sk27,X2) = true,
inference(orient,[status(thm)],[t27404]) ).
cnf(t22850,plain,
true = ifeq(true,true,cong(sk27,X1,X2,sk27),true),
inference(cp,[status(thm)],[t268,t22846]) ).
cnf(t27453,plain,
true = cong(sk27,X1,X2,sk27),
inference(step,[status(thm)],[t22850,t256]) ).
cnf(t23148,plain,
cong(sk27,X1,X2,sk27) = true,
inference(orient,[status(thm)],[t27453]) ).
cnf(t23152,plain,
true = ifeq(true,true,cong(X1,sk27,sk27,X2),true),
inference(cp,[status(thm)],[t266,t23148]) ).
cnf(t27474,plain,
true = cong(X1,sk27,sk27,X2),
inference(step,[status(thm)],[t23152,t256]) ).
cnf(t23441,plain,
cong(X1,sk27,sk27,X2) = true,
inference(orient,[status(thm)],[t27474]) ).
cnf(t23445,plain,
true = ifeq(true,true,cong(X1,sk27,X2,sk27),true),
inference(cp,[status(thm)],[t268,t23441]) ).
cnf(t27488,plain,
true = cong(X1,sk27,X2,sk27),
inference(step,[status(thm)],[t23445,t256]) ).
cnf(t23726,plain,
cong(X1,sk27,X2,sk27) = true,
inference(orient,[status(thm)],[t27488]) ).
cnf(t25566,plain,
true = ifeq(true,true,midp(X1,sk27,sk27),true),
inference(cp,[status(thm)],[t25549,t23726]) ).
cnf(t27667,plain,
true = midp(X1,sk27,sk27),
inference(step,[status(thm)],[t25566,t256]) ).
cnf(t25580,plain,
midp(X1,sk27,sk27) = true,
inference(orient,[status(thm)],[t27667]) ).
cnf(t25581,plain,
true = ifeq(true,true,midp(X1,X2,X3),true),
inference(cp,[status(thm)],[t22534,t25580]) ).
cnf(t27675,plain,
true = midp(X1,X2,X3),
inference(step,[status(thm)],[t25581,t256]) ).
cnf(t25644,plain,
midp(X1,X2,X3) = true,
inference(orient,[status(thm)],[t27675]) ).
cnf(t27676,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t6292,t25644]) ).
cnf(t27677,plain,
false = true,
inference(step,[status(thm)],[t27676,t256]) ).
cnf(t25645,plain,
false = true,
inference(rw,[status(thm)],[t27677]) ).
cnf(t25652,plain,
false = true,
inference(orient,[status(thm)],[t25645]) ).
cnf(t27693,plain,
cong(sk28,sk27,sk28,sk26) = true,
inference(step,[status(thm)],[t3533,t25652]) ).
cnf(t25653,plain,
cong(sk28,sk27,sk28,sk26) = true,
inference(orient,[status(thm)],[t27693]) ).
cnf(goal_0,negated_conjecture,
cong(sk28,sk27,sk28,sk26) != true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t25653]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO587+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 12:31:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 136.07/17.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 136.07/17.87 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------