%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL031+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 02:36:56 PM UTC 2026
% Result : Theorem 88.89s 28.87s
% Output : CNFRefutation 88.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 50 unt; 0 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 72 !; 4 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(f14,conjecture,
! [X0,X1] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one )
=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one )
=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one
& one != join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
? [X0,X1] :
( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one
& one != join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( one = join(composition(converse(sK1),sK1),one)
& one = join(composition(converse(sK0),sK0),one)
& one != join(composition(converse(composition(sK0,sK1)),composition(sK0,sK1)),one) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f17]) ).
fof(f19,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f25,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f32,plain,
one = join(composition(converse(sK1),sK1),one),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
one = join(composition(converse(sK0),sK0),one),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
one != join(composition(converse(composition(sK0,sK1)),composition(sK0,sK1)),one),
inference(cnf_transformation,[],[f18]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f19]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f24]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(cnf_transformation,[],[f25]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f26]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_61,negated_conjecture,
join(composition(converse(composition(sK0,sK1)),composition(sK0,sK1)),one) != one,
inference(cnf_transformation,[],[f34]) ).
tcf(c_62,negated_conjecture,
join(composition(converse(sK0),sK0),one) = one,
inference(cnf_transformation,[],[f33]) ).
tcf(c_63,negated_conjecture,
join(composition(converse(sK1),sK1),one) = one,
inference(cnf_transformation,[],[f32]) ).
tcf(c_78,negated_conjecture,
join(one,composition(converse(composition(sK0,sK1)),composition(sK0,sK1))) != one,
inference(theory_normalisation,[status(thm)],[c_61,c_50,c_49]) ).
tcf(c_79,negated_conjecture,
join(one,composition(converse(sK0),sK0)) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_80,negated_conjecture,
join(one,composition(converse(sK1),sK1)) = one,
inference(theory_normalisation,[status(thm)],[c_63,c_50,c_49]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_259,plain,
! [X0: $i] : join(one,join(composition(converse(sK1),sK1),X0)) = join(one,X0),
inference(superposition,[status(thm)],[c_80,c_50]) ).
tcf(c_464,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_506,plain,
! [X0: $i] : join(one,composition(join(converse(sK1),X0),sK1)) = join(one,composition(X0,sK1)),
inference(superposition,[status(thm)],[c_54,c_259]) ).
tcf(c_555,plain,
! [X0: $i] : join(one,composition(converse(join(sK1,X0)),sK1)) = join(one,composition(converse(X0),sK1)),
inference(superposition,[status(thm)],[c_56,c_506]) ).
tcf(c_2568,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_245]) ).
tcf(c_2590,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[c_2568,c_55]) ).
tcf(c_2613,plain,
! [X0: $i,X1: $i] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(superposition,[status(thm)],[c_2590,c_54]) ).
tcf(c_2615,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_2590,c_53]) ).
tcf(c_2622,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_2590,c_464]) ).
tcf(c_2623,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_2622,c_2590]) ).
tcf(c_13130,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(light_normalisation,[status(thm)],[c_2613,c_2615]) ).
tcf(c_13141,plain,
! [X0: $i] : join(X0,composition(composition(converse(sK0),sK0),X0)) = composition(one,X0),
inference(superposition,[status(thm)],[c_79,c_13130]) ).
tcf(c_13261,plain,
! [X0: $i] : join(X0,composition(converse(sK0),composition(sK0,X0))) = X0,
inference(demodulation,[status(thm)],[c_13141,c_52,c_2623]) ).
tcf(c_15703,plain,
join(one,composition(converse(composition(converse(sK0),composition(sK0,sK1))),sK1)) = join(one,composition(converse(sK1),sK1)),
inference(superposition,[status(thm)],[c_13261,c_555]) ).
tcf(c_15710,plain,
join(one,composition(converse(composition(sK0,sK1)),composition(sK0,sK1))) = one,
inference(demodulation,[status(thm)],[c_15703,c_52,c_80,c_245]) ).
tcf(c_15711,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15710,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL031+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.43 % Computer : n002.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Thu Sep 24 07:29:04 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.50 Running first-order theorem proving
% 0.18/0.50 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.27/0.52
% 0.27/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.27/0.52
% 0.27/0.52 % Detected problem language: tptp
% 0.27/0.54 % Proving...
% 88.89/28.87 % SZS status Started for theBenchmark.p
% 88.89/28.87 % SZS status Theorem for theBenchmark.p
% 88.89/28.87
% 88.89/28.87 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 88.89/28.87
% 88.89/28.87 % ------ iProver source info
% 88.89/28.87
% 88.89/28.87 % git: date: 2026-07-19 20:42:38 +0200
% 88.89/28.87 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 88.89/28.87 % git: non_committed_changes: false
% 88.89/28.87
% 88.89/28.87 % ------ Parsing...
% 88.89/28.87 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 88.89/28.87
% 88.89/28.87 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 88.89/28.87
% 88.89/28.87 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 88.89/28.87
% 88.89/28.87 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 88.89/28.87 % ------ Proving...
% 88.89/28.87 % ------ Problem Properties
% 88.89/28.87
% 88.89/28.87 %
% 88.89/28.87 % clauses 15
% 88.89/28.87 % conjectures 3
% 88.89/28.87 % EPR 0
% 88.89/28.87 % Horn 15
% 88.89/28.87 % unary 15
% 88.89/28.87 % binary 0
% 88.89/28.87 % lits 15
% 88.89/28.87 % lits eq 15
% 88.89/28.87 % fd_pure 0
% 88.89/28.87 % fd_pseudo 0
% 88.89/28.87 % fd_cond 0
% 88.89/28.87 % fd_pseudo_cond 0
% 88.89/28.87 % AC symbols 1
% 88.89/28.87
% 88.89/28.87 % ------ Input Options Time Limit: Unbounded
% 88.89/28.87
% 88.89/28.87
% 88.89/28.87 % ------
% 88.89/28.87 % Current options:
% 88.89/28.87 % ------
% 88.89/28.87
% 88.89/28.87
% 88.89/28.87 %
% 88.89/28.87
% 88.89/28.87 % ------ Proving...
% 88.89/28.87 %
% 88.89/28.87
% 88.89/28.87 % SZS status Theorem for theBenchmark.p
% 88.89/28.87
% 88.89/28.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 88.89/28.87
% 88.89/28.87
%------------------------------------------------------------------------------