%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG008-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 02:38:10 PM UTC 2026
% Result : Unsatisfiable 6.27s 1.75s
% Output : CNFRefutation 6.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 80 ( 68 unt; 1 def)
% Number of atoms : 269 ( 67 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 77 ( 41 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 143 ( 0 sgn 143 !; 0 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
fof(f18,axiom,
! [X0] : product(X0,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_identity_x_is_identity) ).
fof(f19,axiom,
! [X0] : product(additive_identity,X0,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_times_x_is_identity) ).
fof(f20,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_squared_is_x) ).
fof(f21,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f22,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
tcf(c_71,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_72,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_76,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_88,plain,
! [X0: $i] : product(X0,additive_identity,additive_identity),
inference(cnf_transformation,[],[f18]) ).
tcf(c_89,plain,
! [X0: $i] : product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[],[f19]) ).
tcf(c_90,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f20]) ).
tcf(c_91,plain,
product(a,b,c),
inference(cnf_transformation,[],[f21]) ).
tcf(c_92,negated_conjecture,
~ product(b,a,c),
inference(cnf_transformation,[],[f22]) ).
tcf(c_101,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_102,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(well_definedness,[status(thm)],[c_89]) ).
tcf(c_103,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(well_definedness,[status(thm)],[c_90]) ).
tcf(c_104,plain,
multiply(a,b) = c,
inference(well_definedness,[status(thm)],[c_91]) ).
tcf(c_105,plain,
multiply(b,a) != c,
inference(well_definedness,[status(thm)],[c_92]) ).
tcf(c_106,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_71]) ).
tcf(c_107,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_72]) ).
tcf(c_111,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_76]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( add(X2,X5) = X4 )
| ( add(X1,X5) != X3 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_78]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X0,X5) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X1,X3) != X5 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_83]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X5,X1) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X0,X3) != X5 )
| ( multiply(X3,X1) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_85]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_116]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_114]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_128]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_124]) ).
tcf(c_302,definition,
iPr_def_10 = multiply(b,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_303,plain,
iPr_def_10 != c,
inference(demodulation,[status(thm)],[c_105,c_302]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_258,c_252]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_111,c_258]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(superposition,[status(thm)],[c_258,c_111]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(additive_inverse(X0),X1)) = multiply(additive_identity,X1),
inference(superposition,[status(thm)],[c_111,c_260]) ).
tcf(c_455,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,additive_inverse(X1))) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_111,c_262]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,additive_inverse(X1))) = additive_identity,
inference(light_normalisation,[status(thm)],[c_455,c_101]) ).
tcf(c_497,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_387,c_106]) ).
tcf(c_502,plain,
! [X0: $i] : add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
inference(superposition,[status(thm)],[c_111,c_497]) ).
tcf(c_514,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_502,c_107]) ).
tcf(c_566,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(additive_inverse(X1),X0))) = add(X1,additive_identity),
inference(superposition,[status(thm)],[c_389,c_497]) ).
tcf(c_588,plain,
! [X0: $i] : add(X0,multiply(X0,additive_inverse(X0))) = additive_identity,
inference(superposition,[status(thm)],[c_103,c_470]) ).
tcf(c_655,plain,
! [X0: $i] : multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0))) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_588,c_497]) ).
tcf(c_657,plain,
! [X0: $i] : multiply(additive_inverse(X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_655,c_107,c_514]) ).
tcf(c_1246,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(additive_inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_566,c_107]) ).
tcf(c_1260,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_514,c_1246]) ).
tcf(c_1417,plain,
! [X0: $i,X1: $i] : additive_inverse(add(X0,additive_inverse(X1))) = add(X1,additive_inverse(X0)),
inference(superposition,[status(thm)],[c_1260,c_497]) ).
tcf(c_1620,plain,
! [X0: $i,X1: $i] : add(additive_inverse(X0),additive_inverse(X1)) = additive_inverse(add(X1,X0)),
inference(superposition,[status(thm)],[c_514,c_1417]) ).
tcf(c_1672,plain,
! [X0: $i,X1: $i] : multiply(add(additive_inverse(X0),additive_inverse(X1)),add(X1,X0)) = add(X1,X0),
inference(superposition,[status(thm)],[c_1620,c_657]) ).
tcf(c_1738,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(additive_inverse(X0),X1)) = additive_identity,
inference(demodulation,[status(thm)],[c_436,c_102]) ).
tcf(c_1788,plain,
! [X0: $i] : add(multiply(X0,X0),X0) = additive_identity,
inference(superposition,[status(thm)],[c_657,c_1738]) ).
tcf(c_1818,plain,
! [X0: $i] : add(X0,multiply(X0,X0)) = additive_identity,
inference(theory_normalisation,[status(thm)],[c_1788,c_258,c_252]) ).
tcf(c_1819,plain,
! [X0: $i] : add(X0,X0) = additive_identity,
inference(light_normalisation,[status(thm)],[c_1818,c_103]) ).
tcf(c_1919,plain,
! [X0: $i] : add(X0,additive_identity) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_1819,c_497]) ).
tcf(c_1923,plain,
! [X0: $i] : additive_inverse(X0) = X0,
inference(light_normalisation,[status(thm)],[c_1919,c_107]) ).
tcf(c_1941,plain,
! [X0: $i,X1: $i] : add(X0,add(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_497,c_1923]) ).
tcf(c_5792,plain,
! [X0: $i,X1: $i] : multiply(add(X0,additive_inverse(X1)),add(X1,X0)) = add(X1,X0),
inference(light_normalisation,[status(thm)],[c_1672,c_1923]) ).
tcf(c_5793,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,add(multiply(X0,X1),multiply(X1,X0)))) = add(X1,X0),
inference(demodulation,[status(thm)],[c_5792,c_103,c_252,c_258,c_260,c_262,c_357,c_1923]) ).
tcf(c_5832,plain,
add(a,add(b,add(multiply(a,b),iPr_def_10))) = add(b,a),
inference(superposition,[status(thm)],[c_302,c_5793]) ).
tcf(c_5894,plain,
add(iPr_def_10,add(a,add(b,multiply(a,b)))) = add(a,b),
inference(theory_normalisation,[status(thm)],[c_5832,c_258,c_252]) ).
tcf(c_5895,plain,
add(iPr_def_10,add(a,add(b,c))) = add(a,b),
inference(light_normalisation,[status(thm)],[c_5894,c_104]) ).
tcf(c_6031,plain,
add(a,add(b,c)) = add(iPr_def_10,add(a,b)),
inference(superposition,[status(thm)],[c_5895,c_1941]) ).
tcf(c_6066,plain,
add(a,add(iPr_def_10,add(a,b))) = add(b,c),
inference(superposition,[status(thm)],[c_6031,c_1941]) ).
tcf(c_6082,plain,
add(iPr_def_10,add(a,add(a,b))) = add(b,c),
inference(theory_normalisation,[status(thm)],[c_6066,c_258,c_252]) ).
tcf(c_6104,plain,
add(b,c) = add(iPr_def_10,b),
inference(demodulation,[status(thm)],[c_6082,c_1941]) ).
tcf(c_6107,plain,
add(b,add(iPr_def_10,b)) = c,
inference(superposition,[status(thm)],[c_6104,c_1941]) ).
tcf(c_6122,plain,
add(iPr_def_10,add(b,b)) = c,
inference(theory_normalisation,[status(thm)],[c_6107,c_258,c_252]) ).
tcf(c_6164,plain,
add(iPr_def_10,add(b,b)) != iPr_def_10,
inference(demodulation,[status(thm)],[c_303,c_6122]) ).
tcf(c_6165,plain,
$false,
inference(ground_joinability,[status(thm)],[c_6164,c_107,c_1819]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 07:44:24 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 6.27/1.75 % SZS status Started for theBenchmark.p
% 6.27/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 6.27/1.75
% 6.27/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.27/1.75
% 6.27/1.75 % ------ iProver source info
% 6.27/1.75
% 6.27/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 6.27/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.27/1.75 % git: non_committed_changes: false
% 6.27/1.75
% 6.27/1.75 % ------ Parsing...% successful
% 6.27/1.75
% 6.27/1.75
% 6.27/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.27/1.75
% 6.27/1.75 % ------ Preprocessing... sup_sim: 15 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.27/1.75
% 6.27/1.75 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 6.27/1.75 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.27/1.75
% 6.27/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 6.27/1.75 % ------ Proving...
% 6.27/1.75 % ------ Problem Properties
% 6.27/1.75
% 6.27/1.75 %
% 6.27/1.75 % clauses 14
% 6.27/1.75 % conjectures 0
% 6.27/1.75 % EPR 1
% 6.27/1.75 % Horn 14
% 6.27/1.75 % unary 14
% 6.27/1.75 % binary 0
% 6.27/1.75 % lits 14
% 6.27/1.75 % lits eq 14
% 6.27/1.75 % fd_pure 0
% 6.27/1.75 % fd_pseudo 0
% 6.27/1.75 % fd_cond 0
% 6.27/1.75 % fd_pseudo_cond 0
% 6.27/1.75 % AC symbols 1
% 6.27/1.75
% 6.27/1.75 % ------ Schedule UEQ
% 6.27/1.75
% 6.27/1.75 % ------ Option_UEQ Time Limit: 10.
% 6.27/1.75
% 6.27/1.75
% 6.27/1.75 % ------
% 6.27/1.75 % Current options:
% 6.27/1.75 % ------
% 6.27/1.75
% 6.27/1.75
% 6.27/1.75 %
% 6.27/1.75
% 6.27/1.75 % ------ Proving...
% 6.27/1.75 %
% 6.27/1.75
% 6.27/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 6.27/1.75
% 6.27/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.27/1.75
% 6.27/1.75
%------------------------------------------------------------------------------